## Friday, January 31, 2014

### 5446

5446 = 2 x 7  x 389.

5446 is the number of ways to arrange the numbers 1 to 10 around a circle so that the sums of adjacent numbers are distinct.

5446 is 41114 in base 6 (A043013).

The 5446th prime (53,407) minus 5446 is a square (A064370): 53407 - 5446 = 47961 = 2192.

## Thursday, January 30, 2014

### 1435

1435 = 5 x 7 x 41.

1435 is the product of three distinct primes and the sum of its prime factors (5 + 7 + 41 = 53) is a prime (A176877).

1435 is a vampire number; it has a factorization (35 x 41) that uses digits from the number itself (A014575).

1435 and its reversal (5341) are both multiples of 7 (A062901).

The 1435th triangular number (1,030,330) contains only the digits {0, 1, 3} (A119036).

1435 is 747 in base 14.

1435 divides 834 - 1.

Source: Number Gossip

## Wednesday, January 29, 2014

### 7356

7356 = 2 x 2 x 3 x 613.

7356 is a value of n for which 5n (36780) and 7n (51492) together use each digit exactly once.

7356 is 5588 in base 11.

7356 divides 354 - 1.

7356 is a number that cannot be written as a sum of three squares.

## Tuesday, January 28, 2014

### 7174

7174 = 2 x 17 x 211.

7174 is the maximum number of pieces into which 34 slices cut a torus (A003600).

7174 is the sum of the first 45 palindromes (A046489).

7174 is 26626 in base 7 and 16006 in base 8.

7174 divides 6714 - 1.

## Monday, January 27, 2014

### 5160

5160 = 2 x 2 x 2 x 3 x 5 x 43.

5160 is a hendecagonal pyramidal number (A007586).

5160 is a number that can be expressed as the difference of the squares of primes in exactly four distinct ways (A092000). It can be expressed as the difference of the squares of consecutive primes in just two distinct ways (A090784).

5160 is the sum of nonconsecutive factorial numbers (A060112): 5160 = 7! + 5!

5160 is a number n such that 2n + 1, 4n + 1, 8n + 1, and 16n + 1 are all primes (A124412).

5160 is 21021 in base 7 (A037524).

5160 and the square of 5160 use only the digits 0, 1, 2, 5, and 6 (A136823).

5160 and its reversal 615 are both multiples of 15 (A062905).

5160 divides 496 - 1.

## Friday, January 24, 2014

### 8128

8128 = 2 x 2 x 2 x 2 x 2 x 2 x 127.

8128 is a perfect number (27 - 1(27 - 1)), associated with the Mersenne prime 127 = 27 - 1 (A000396). It is the largest perfect number whose index (4) is equal to the number of digits.

8128 is the 127th triangular number; it is the sum of the first 127 integers. 8128 is the 64th hexagonal number. It is also a centered nonagonal number (A060544).

8128 divides 6314 - 1.

Source: Number Gossip

## Thursday, January 23, 2014

### 1081

1081 = 23 x 47.

1081 is the 46th triangular number (the sum of the first 46 integers) (A000217 and A068443). It is also a centered nonagonal number (A060544).

1081 is a member of the Padovan sequence (A000931).

1081 is a concentric dodecagonal number (A195143).

1081 is the sum of 11 consecutive primes (A127338).

1081 is the smallest semiprime and brilliant number that is prime when reversed and turned upside down.

1081 divides 932 - 1.

Source: Prime Curios!

## Wednesday, January 22, 2014

### 8080

8080 = 2 x 2 x 2 x 2 x 5 x 101.

8080 has a square root that has four 8s immediately after the decimal point.

8080 is the number of points on the surface of a four-dimensional 10 x 10 x 10 x 10 cube (A008511).

8080 is a number n such that n plus the factorial of the largest digit of n is a square (A095927): 8080 + 8! = 48400 = 2202.

8080 has two representations as a sum of two squares: 8080 = 322 + 842 = 482 + 762.  8080 is the smallest member of a triple of consecutive numbers each of which is the sum of two nonzero squares (A064715 and A073412).

8080 divides 914 - 1. 8080 is the difference of two positive fourth powers (A147857).

## Tuesday, January 21, 2014

### 7246

7246 = 2 x 3623.

7246 is a centered heptagonal number (A069099).

7246 is a semiprime centered triangular number (A184481).

7246 is 16116 in base 8.

27246 + 37246 is a semiprime (A050244).

Source: On-Line Encyclopedia of Integer Sequences

## Friday, January 17, 2014

### 7379

7379 = 47 x 157.

Every divisor of 7379 (except 1) contains the digit 7 (A062676).

7379 is the concatenation of the 21st and 22nd prime (A045533 and A007795 and A103206).

7379 is a semiprime that is the sum of three distinct positive cubes in two or more distinct ways (A180089).

7379 is the number of ways to partition a 12 x 3 grid into three connected equal-area regions (A167243).

7379 divides 4626 - 1.

Source: On-Line Encyclopedia of Integer Sequences

## Thursday, January 16, 2014

### 5914

5914 = 2 x 2957.

5914 = 0! + 1! + 2! + 3! + 4! + 5! + 6! + 7!

5914 has a representation as a sum of two squares: 5914 = 172 + 752.

5914 expressed in base 6 (43214) and in base 8 (13432) uses the digits 1, 2, 3, and 4 (A037435).

## Wednesday, January 15, 2014

### 9686

9686 = 2 x 29 x 167.

9686 is 2113112 in base 4.

9686 is a number that is not the sum of two triangular numbers and a fourth power (A115160).

9686 is the least sum of three distinct nonzero squares in exactly 42 ways (A025415).

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, January 14, 2014

### 1765

1765 =  5 x 353. It is a number with exactly two palindromic prime factors (A046368).

1765 is one more than a perfect square (A002522 and A134406).

1765 is the smallest positive number that can be written as the sum of distinct Fibonacci numbers in 39 ways (A013583).

1765 has two representations as a sum of two squares: 1765 = 12 + 422 = 262 + 332.

1765 is the number of polyominoes without holes consisting of six regular unit 13-gons (A103472).

1765 is the hypotenuse of two primitive Pythagorean triples: 17652 = 842 + 17632 = 4132 + 17162.

1765 divides 424 - 1.

Source: On-Line Encyclopedia of Integer Sequences

## Monday, January 13, 2014

### 5211

5211 = 3 x 3 x 3 x 193.

5211 has a square root (72.18725649309...) whose decimal part starts with the digits 1 to 9 in some order (A034277).

Representations of 5211 in base 5, 7, and 8 use only the digits 1, 2, and 3 (A037431 and A037438).

5211 is a composite number with a digit product of 10 (A199990 and A201057).

5211 and the square of 5211 use only the digits 1, 2, 4, 5, and 7 (A136989).

5211 divides 8518 - 1.

## Friday, January 10, 2014

### 7706

7706 = 2 x 3853.

7706 is the number of binary strings of length 16 with no substrings equal to 0000, 0001, or 0110 (A164411).

7706 has a representation as a sum of two squares: 7706 = 592 + 652.

7706 has the representation 65 - 70.

NGC 7706 is a lenticular galaxy located in Pisces, discovered by John Herschel in 1827.

Source: On-Line Encyclopedia of Integer Sequences

## Thursday, January 9, 2014

### 3516

3516 = 2 x 2 x 3 x 293.

3516 is a centered pentagonal number (A005891).

3516 is a member of the Fibonacci-like sequence beginning with 5 and 12 (A022137).

3516 is a number n such that n + 1, n2 + 1, and n4 + 1 are all primes (A070325). It is a number n such that n2 + 5 and n2 + 7 are twin primes (A127845).

3516 and the square of 3516 use only the digits 1, 2, 3, 5, and 6 (A136974).

Source: On-Line Encyclopedia of Integer Sequences

## Wednesday, January 8, 2014

### 9141

9141 = 3 x 11 x 277.

9141 yields a prime whenever a 1 is inserted anywhere, including the beginning or end (A068679 and A216165).

9141 is the number of ways to partition 230 into distinct positive integers not greater than 30 (A079122).

9141 is a tetrahedral number written backwards (A004161).

9141 is a member of the sequence generated by starting with 1 and repeatedly reversing the digits and adding 65 to get the next term (A118163).

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, January 7, 2014

### 5461

5461 = 43 x 127.

5461 is 1010101010101 in binary (base 2).

5461 is 1111111 in base 4 (A053716). It divides 47 - 1.

5461 is a centered heptagonal number (A069099). It is also an octagonal (star) number (A000567) and a concentric tridecagonal number (A195045).

5461 is a Poulet number.

## Monday, January 6, 2014

### 716

716 = 2 x 2 x 179.

The digits of 716 can be rearranged (180-degree rotations permitted) to form a prime number that divides it.

716 is the number of three-digit numbers that contain at least one prime digit (2, 3, 5, or 7).

716 is the smallest number whose cube (367,061,696) contains four sixes.

716 is 1314 in base 8.

Source: Prime Curios!

## Friday, January 3, 2014

### 8444

8444 = 2 x 2 x 2111. It is a composite number such that its prime factors contain only the digits 1 or 2 (A036302).

8444 is equal to the square of the sum of the first 9 primes minus the sum of the squares of the first 9 primes (A065595).

For 8444, each digit (a composite) minus 1 is a prime, the sum of the digits minus 1 (19) is a prime, and the difference of digits (in absolute value) minus 1 is prime (A058229).

8444 divides 7510 - 1.

8444 is 33422 in base 7. It also uses the same digits in base 5 (232234).

Source: On-Line Encyclopedia of Integer Sequences

## Thursday, January 2, 2014

### 752

752 = 2 x 2 x 2 x 2 x 47. It is the product of the fourth power of a prime and a different prime (A178739).

752 is the sum of distinct factorials (A059590): 752 = 6! + 4! + 3! + 2!

752 is the number of ways of writing 20 as the sum of five squares (A000132).

The sum of the digits of 752 (14) equals the sum of the digits of the 752nd prime (5711) (A033549).

752 is a number that is the sum of no fewer than 17 fourth powers (A099591).

752 is the number of conjugacy classes in the automorphism group of the 11-dimensional hypercube.