A272024 - OEIS

%I #34 May 04 2016 08:50:32

%S 1,3,5,15,11,77,22,176,101,385,77,3718,135,1575,1575,6842,385,31185,

%T 627,53174,8349,17977,1575,966467,6842,53174,37338,526823,5604,

%U 5392783,8349,1505499,147273,386155,147273,64112359,26015,966467,526823,56634173,53174,118114304,75175,26543660,12132164,5392783

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

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

%C 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 Seiichi Manyama, <a href="/A272024/b272024.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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 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 Table[PartitionsP@ DivisorSigma[1, n], {n, 46}] (* _Michael De Vlieger_, Apr 19 2016 *)

%o (PARI) a(n) = numbpart(sigma(n)); \\ _Michel Marcus_, Apr 19 2016

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

%K nonn

%O 1,2

%A _Omar E. Pol_, Apr 19 2016