A079125 Number of ways to partition the sum of all divisors of n (sigma(n), A000203) into distinct positive integers not greater than n.

1, 1, 1, 2, 3, 5, 5, 13, 13, 27, 14, 89, 21, 89, 97, 230, 45, 613, 63, 980, 347, 580, 121, 6663, 330, 1289, 1043, 5847, 295, 26488, 389, 12813, 2800, 5411, 2840, 156304, 863, 10433, 6939, 161711, 1425, 272499, 1815, 103738, 61469, 35448, 2909, 2475011

Offset: 1

Author

Reinhard Zumkeller, Dec 27 2002

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A079126, A000009, A079122, A079124, A067953.

Programs

Mathematica

a[n_] := Module[{sum = DivisorSigma[1, n], x}, CoefficientList[Product[1 + x^i, {i, 1, n}], x][[1 + sum]]]; Array[a, 50] (* Amiram Eldar, Apr 15 2025 *)

PARI

a(n)=my(v=partitions(sigma(n),n));sum(i=1,#v,#vecsort(v[i],,8)==#v[i]) \\ Charles R Greathouse IV, Feb 14 2013

Formula

a(n) = b(0, n), b(m, n) = 1 + Sum_{m < i < j < n & i+j = sigma(n)} b(i, j).