cp's OEIS Frontend

A352493 Number of non-constant integer partitions of n into prime parts with prime multiplicities.

%I A352493 #10 Mar 31 2022 03:04:19
%S A352493 0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,3,0,1,4,5,3,1,3,5,7,3,5,6,8,8,11,7,6,
%T A352493 8,15,14,14,10,15,17,21,18,23,20,28,25,31,27,35,32,33,37,46,41,50,45,
%U A352493 58,56,63,59,78,69,76,81,85,80,103,107,111,114,127
%N A352493 Number of non-constant integer partitions of n into prime parts with prime multiplicities.
%e A352493 The a(n) partitions for selected n (B = 11):
%e A352493 n = 10    16       19        20         25          28
%e A352493    ---------------------------------------------------------------
%e A352493     3322  5533     55333     7733       77722       BB33
%e A352493           55222    55522     77222      5533333     BB222
%e A352493           3322222  3333322   553322     5553322     775522
%e A352493                    33322222  5522222    55333222    55533322
%e A352493                              332222222  55522222    772222222
%e A352493                                         333333322   3322222222222
%e A352493                                         3333322222
%t A352493 Table[Length[Select[IntegerPartitions[n], !SameQ@@#&&And@@PrimeQ/@#&& And@@PrimeQ/@Length/@Split[#]&]],{n,0,30}]
%Y A352493 Constant partitions are counted by A001221, ranked by A000961.
%Y A352493 Non-constant partitions are counted by A144300, ranked A024619.
%Y A352493 The constant version is A230595, ranked by A352519.
%Y A352493 This is the non-constant case of A351982, ranked by A346068.
%Y A352493 These partitions are ranked by A352518.
%Y A352493 A000040 lists the primes.
%Y A352493 A000607 counts partitions into primes, ranked by A076610.
%Y A352493 A001597 lists perfect powers, complement A007916.
%Y A352493 A038499 counts partitions of prime length.
%Y A352493 A053810 lists primes to primes.
%Y A352493 A055923 counts partitions with prime multiplicities, ranked by A056166.
%Y A352493 A257994 counts prime indices that are themselves prime.
%Y A352493 A339218 counts powerful partitions into prime parts, ranked by A352492.
%Y A352493 Cf. A000005, A007690, A031368, A035444, A052485, A056239, A066208, A089723, A114639, A320628, A330945.
%K A352493 nonn
%O A352493 0,17
%A A352493 _Gus Wiseman_, Mar 24 2022