1305 = 3 x 3 x 5 x 29.
1305 has two representations as a sum of two squares: 1305 = 32 + 362 = 242 + 272.
1305 is the number of graphs with 11 vertices and 9 edges.
1305 is 909 in base 12.
1305 is a number n such that n2 (1703025) can be obtained by inserting internal (but not necessarily contiguous) digits (A046851).
Source: What's Special About This Number?
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