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

1,4

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A342421 A319631 A097453 * A146305 A395254 A342437

Adjacent sequences: A079122 A079123 A079124 * A079126 A079127 A079128

Keyword

nonn

Author

Reinhard Zumkeller, Dec 27 2002

Status

approved