cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A272024 #34 May 04 2016 08:50:32
%S A272024 1,3,5,15,11,77,22,176,101,385,77,3718,135,1575,1575,6842,385,31185,
%T A272024 627,53174,8349,17977,1575,966467,6842,53174,37338,526823,5604,
%U A272024 5392783,8349,1505499,147273,386155,147273,64112359,26015,966467,526823,56634173,53174,118114304,75175,26543660,12132164,5392783
%N A272024 Number of partitions of the sum of the divisors of n.
%C A272024 Also number of partitions of the total number of parts in the partitions of n into equal parts.
%C A272024 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.
%H A272024 Seiichi Manyama, <a href="/A272024/b272024.txt">Table of n, a(n) for n = 1..10000</a>
%F A272024 a(n) = p(sigma(n)) = A000041(A000203(n)).
%e A272024 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.
%e A272024 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.
%t A272024 Table[PartitionsP@ DivisorSigma[1, n], {n, 46}] (* _Michael De Vlieger_, Apr 19 2016 *)
%o A272024 (PARI) a(n) = numbpart(sigma(n)); \\ _Michel Marcus_, Apr 19 2016
%Y A272024 Cf. A000041, A000203, A056538, A058699, A072861, A139041, A272209.
%K A272024 nonn
%O A272024 1,2
%A A272024 _Omar E. Pol_, Apr 19 2016