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A352493
Number of non-constant integer partitions of n into prime parts with prime multiplicities.
3
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
0,17
EXAMPLE
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
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !SameQ@@#&&And@@PrimeQ/@#&& And@@PrimeQ/@Length/@Split[#]&]], {n, 0, 30}]
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.
Sequence in context: A124323 A250104 A220421 * A106683 A139601 A213191
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 24 2022
STATUS
approved