login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
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
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
KEYWORD
nonn
AUTHOR
Omar E. Pol, Apr 19 2016
STATUS
approved