cp's OEIS Frontend

A325132 Number of integer partitions of n where the multiplicity of each part k is at least prime(k).

%I A325132 #10 Nov 29 2020 08:18:57
%S A325132 1,0,1,1,1,1,2,1,3,2,4,3,5,4,6,6,7,7,10,8,11,12,12,14,17,16,20,22,24,
%T A325132 26,31,31,37,39,43,46,54,53,63,65,73,75,87,87,100,102,115,117,133,134,
%U A325132 151,155,172,176,197,202,223,231,254,262,290,298,327,341,370
%N A325132 Number of integer partitions of n where the multiplicity of each part k is at least prime(k).
%C A325132 The Heinz numbers of these partitions are given by A054744.
%F A325132 G.f.: Product_{k>=1} (1 + x^(prime(k)*k) / (1 - x^k)). - _Ilya Gutkovskiy_, Nov 28 2020
%e A325132 The first few terms count the following integer partitions:
%e A325132    0: ()
%e A325132    2: (11)
%e A325132    3: (111)
%e A325132    4: (1111)
%e A325132    5: (11111)
%e A325132    6: (222)
%e A325132    6: (111111)
%e A325132    7: (1111111)
%e A325132    8: (2222)
%e A325132    8: (22211)
%e A325132    8: (11111111)
%e A325132    9: (222111)
%e A325132    9: (111111111)
%e A325132   10: (22222)
%e A325132   10: (222211)
%e A325132   10: (2221111)
%e A325132   10: (1111111111)
%e A325132   11: (2222111)
%e A325132   11: (22211111)
%e A325132   11: (11111111111)
%e A325132   12: (222222)
%e A325132   12: (2222211)
%e A325132   12: (22221111)
%e A325132   12: (222111111)
%e A325132   12: (111111111111)
%t A325132 Table[Length[Select[IntegerPartitions[n],And@@Table[Count[#,i]>=Prime[i],{i,Union[#]}]&]],{n,0,30}]
%Y A325132 Cf. A052335, A054744, A062457, A087153, A117144, A324525, A324572.
%K A325132 nonn
%O A325132 0,7
%A A325132 _Gus Wiseman_, Apr 01 2019