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A352493
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Number of non-constant integer partitions of n into prime parts with prime multiplicities.
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3
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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
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OFFSET
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0,17
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], !SameQ@@#&&And@@PrimeQ/@#&& And@@PrimeQ/@Length/@Split[#]&]], {n, 0, 30}]
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CROSSREFS
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These partitions are ranked by A352518.
A038499 counts partitions of prime length.
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.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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