

A272024


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


3



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
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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: A180620 A277323 A160046 * A111869 A093015 A243940
Adjacent sequences: A272021 A272022 A272023 * A272025 A272026 A272027


KEYWORD

nonn


AUTHOR

Omar E. Pol, Apr 19 2016


STATUS

approved



