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

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, 8, 15, 14, 14, 10, 15, 17, 21, 18, 23, 20, 28, 25, 31, 27, 35, 32, 33, 37, 46, 41, 50, 45, 58, 56, 63, 59, 78, 69, 76, 81, 85, 80, 103, 107, 111, 114, 127

Offset: 0

Author

Gus Wiseman, Mar 24 2022

Keywords

• nonn

Examples

			The a(n) partitions for selected n (B = 11):
n = 10    16       19        20         25          28
   ---------------------------------------------------------------
    3322  5533     55333     7733       77722       BB33
          55222    55522     77222      5533333     BB222
          3322222  3333322   553322     5553322     775522
                   33322222  5522222    55333222    55533322
                             332222222  55522222    772222222
                                        333333322   3322222222222
                                        3333322222
		

Crossrefs

Constant partitions are counted by A001221, ranked by A000961.

Non-constant partitions are counted by A144300, ranked A024619.

The constant version is A230595, ranked by A352519.

This is the non-constant case of A351982, ranked by A346068.

These partitions are ranked by A352518.

A000040 lists the primes.

A000607 counts partitions into primes, ranked by A076610.

A001597 lists perfect powers, complement A007916.

A038499 counts partitions of prime length.

A053810 lists primes to primes.

A055923 counts partitions with prime multiplicities, ranked by A056166.

A257994 counts prime indices that are themselves prime.

A339218 counts powerful partitions into prime parts, ranked by A352492.

Cf. A000005, A007690, A031368, A035444, A052485, A056239, A066208, A089723, A114639, A320628, A330945.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n], !SameQ@@#&&And@@PrimeQ/@#&& And@@PrimeQ/@Length/@Split[#]&]],{n,0,30}]