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 A387327 #6 Sep 05 2025 23:46:00
%S A387327 1,2,3,4,7,6,15,8,9,14,56,12,101,30,21,16,297,18,490,28,45,112,1255,
%T A387327 24,49,202,27,60,4565,42,6842,32,168,594,105,36,21637,980,303,56,
%U A387327 44583,90,63261,224,63,2510,124754,48,225,98,891,404,329931,54,392,120
%N A387327 Number of ways to choose an integer partition of each prime factor of n (with multiplicity).
%e A387327 The a(1) = 1 through a(7) = 15 ways:
%e A387327 (1) (2) (3) (2)(2) (5) (2)(3) (7)
%e A387327 (11) (21) (11)(2) (32) (11)(3) (43)
%e A387327 (111) (2)(11) (41) (2)(21) (52)
%e A387327 (11)(11) (221) (11)(21) (61)
%e A387327 (311) (2)(111) (322)
%e A387327 (2111) (11)(111) (331)
%e A387327 (11111) (421)
%e A387327 (511)
%e A387327 (2221)
%e A387327 (3211)
%e A387327 (4111)
%e A387327 (22111)
%e A387327 (31111)
%e A387327 (211111)
%e A387327 (1111111)
%t A387327 Table[Length[Tuples[IntegerPartitions/@Flatten[ConstantArray@@@FactorInteger[n]]]],{n,30}]
%Y A387327 For constant partitions we have A061142, for prime indices A355731.
%Y A387327 For prime indices instead of factors we have A299200.
%Y A387327 The version for distinct choices is A387133, zeros A387326.
%Y A387327 A000041 counts integer partitions, strict A000009.
%Y A387327 A112798 lists prime indices, row sums A056239 or A066328, lengths A001222.
%Y A387327 A387110 counts choices of distinct distinct integer partitions of each prime index.
%Y A387327 Cf. A063834, A120383, A299201, A335433, A335448, A355741, A357977, A383706, A387115, A387120, A387136.
%K A387327 nonn,new
%O A387327 1,2
%A A387327 _Gus Wiseman_, Sep 05 2025