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.
%I A330954 #10 Jan 18 2020 07:41:17
%S A330954 0,0,0,0,0,0,1,0,2,3,4,2,3,9,8,18,15,25,35,44,50,70,71,93,141,158,226,
%T A330954 286,337,439,532,648,789,1013,1261,1454,1776,2176,2701,3258,3823,4606,
%U A330954 5521,6613,7810,9202,11074,13145,15498,18413,21818,25774,30481,35718
%N A330954 Number of integer partitions of n whose product is divisible by the sum of primes of their parts.
%e A330954 The a(7) = 1 through a(15) = 8 partitions (empty column not shown):
%e A330954 43 63 541 83 552 6322 4433 5532
%e A330954 441 4222 3332 6411 7411 7322 6522
%e A330954 222211 5222 62221 44321 84111
%e A330954 33221 63311 333222
%e A330954 65111 432222
%e A330954 72221 3322221
%e A330954 433211 32222211
%e A330954 4322111 333111111
%e A330954 322211111
%e A330954 For example, the partition (3,3,2,2,1) has product 3 * 3 * 2 * 2 * 1 = 36 and sum of primes 5 + 5 + 3 + 3 + 2 = 18, and 36 is divisible by 18, so (3,3,2,2,1) is counted under a(11).
%t A330954 Table[Length[Select[IntegerPartitions[n],Divisible[Times@@#,Plus@@Prime/@#]&]],{n,30}]
%Y A330954 The Heinz numbers of these partitions are given by A331378.
%Y A330954 Partitions whose product is divisible by their sum are A057568.
%Y A330954 Numbers divisible by the sum of their prime indices are A324851.
%Y A330954 Partitions whose sum of primes divides their product of primes are A330953.
%Y A330954 Partitions whose sum of primes divides of their product are A331381.
%Y A330954 Partitions whose product equals their sum of primes are A331383.
%Y A330954 Cf. A000040, A001414, A036844, A056239, A324850, A326149, A330950, A331379, A331382, A331384, A331415, A331416.
%K A330954 nonn
%O A330954 1,9
%A A330954 _Gus Wiseman_, Jan 15 2020