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A351982
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Number of integer partitions of n into prime parts with prime multiplicities.
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8
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1, 0, 0, 0, 1, 0, 2, 0, 0, 1, 3, 0, 1, 1, 3, 3, 3, 0, 1, 4, 5, 5, 3, 3, 5, 8, 5, 5, 6, 8, 8, 11, 7, 8, 10, 17, 14, 14, 12, 17, 17, 21, 18, 23, 20, 28, 27, 31, 27, 36, 32, 35, 37, 46, 41, 52, 45, 60, 58, 63, 59, 78, 71, 76, 81, 87, 80, 103, 107, 113, 114, 127
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OFFSET
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0,7
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LINKS
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EXAMPLE
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The partitions for n = 4, 6, 10, 19, 20, 25:
(22) (33) (55) (55333) (7733) (55555)
(222) (3322) (55522) (77222) (77722)
(22222) (3333322) (553322) (5533333)
(33322222) (5522222) (5553322)
(332222222) (55333222)
(55522222)
(333333322)
(3333322222)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], And@@PrimeQ/@#&&And@@PrimeQ/@Length/@Split[#]&]], {n, 0, 30}]
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CROSSREFS
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The version for just prime multiplicities is A055923, ranked by A056166.
These partitions are ranked by A346068.
A001221 counts constant partitions of prime length, ranked by A053810.
A038499 counts partitions of prime length.
A101436 counts parts of prime signature that are themselves prime.
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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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