A272024 Number of partitions of the sum of the divisors of n.

1, 3, 5, 15, 11, 77, 22, 176, 101, 385, 77, 3718, 135, 1575, 1575, 6842, 385, 31185, 627, 53174, 8349, 17977, 1575, 966467, 6842, 53174, 37338, 526823, 5604, 5392783, 8349, 1505499, 147273, 386155, 147273, 64112359, 26015, 966467, 526823, 56634173, 53174, 118114304, 75175, 26543660, 12132164, 5392783

Offset

1,2

Comments

Also number of partitions of the total number of parts in the partitions of n into equal parts.

Note that one of the partitions of the sum of the divisors of n is also the list of divisors of n in decreasing order, see example.

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

a(n) = p(sigma(n)) = A000041(A000203(n)).

Example

For n = 9 the sum of the divisors of 9 is 1 + 3 + 9 = 13 and the number of partitions of 13 is A000041(13) = 101, so a(9) = 101.
Note that one of the 101 partitions of 13 is [9, 3, 1] and it is also the list of divisors of 9 in decreasing order.

Mathematica

Table[PartitionsP@ DivisorSigma[1, n], {n, 46}] (* Michael De Vlieger, Apr 19 2016 *)

Prog

(PARI) a(n) = numbpart(sigma(n)); \\ Michel Marcus, Apr 19 2016

Crossrefs

Cf. A000041, A000203, A056538, A058699, A072861, A139041, A272209.

Sequence in context: A340194 A353340 A160046 * A111869 A093015 A371450

Adjacent sequences: A272021 A272022 A272023 * A272025 A272026 A272027

Keyword

nonn

Author

Omar E. Pol, Apr 19 2016

Status

approved