A085494 Numbers k having exactly one partition into distinct divisors of k+1.

1, 3, 5, 7, 15, 17, 19, 27, 31, 53, 63, 65, 69, 77, 87, 99, 103, 127, 161, 195, 255, 271, 303, 367, 413, 463, 485, 495, 499, 511, 579, 649, 725, 819, 859, 867, 967, 1013, 1023, 1035, 1147, 1183, 1311, 1315, 1351, 1371, 1375, 1457, 1483, 1503, 1695, 1887, 1951

Offset: 1

Author

Reinhard Zumkeller, Jul 03 2003

Keywords

• nonn

Comments

Includes every 2^k-1 and is therefore infinite. - David W. Wilson, Feb 02 2006

Links

• Amiram Eldar, Table of n, a(n) for n = 1..330

Crossrefs

Cf. A085491, A085499.

Subsequence of A085493.

Programs

Mathematica

q[k_] := Module[{d = Divisors[k+1], x}, CoefficientList[Product[1 + x^i, {i, d}], x][[1+k]] == 1]; Select[Range[2000], q] (* Amiram Eldar, Apr 16 2025 *)

Formula

A085491(a(n)) = 1.

Extensions

More terms from David W. Wilson, Feb 02 2006