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A338903
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Number of integer partitions of the n-th squarefree semiprime into squarefree semiprimes.
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10
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1, 1, 1, 1, 2, 2, 3, 3, 5, 4, 6, 5, 12, 14, 19, 22, 27, 36, 38, 51, 77, 86, 128, 141, 163, 163, 207, 233, 259, 260, 514, 657, 813, 983, 1010, 1215, 1255, 1720, 2112, 2256, 3171, 3370, 3499, 3864, 4103, 6292, 7313, 7620, 8374, 10650, 17579, 18462, 23034, 25180
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OFFSET
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1,5
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COMMENTS
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A squarefree semiprime (A006881) is a product of any two distinct prime numbers.
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LINKS
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FORMULA
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EXAMPLE
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The a(n) partitions for n = 1, 5, 7, 9, 10, 11, 13:
6 21 26 34 35 38 46
15,6 14,6,6 22,6,6 21,14 26,6,6 34,6,6
10,10,6 14,14,6 15,14,6 22,10,6 26,14,6
14,10,10 15,10,10 14,14,10 21,15,10
10,6,6,6,6 14,6,6,6,6 22,14,10
10,10,6,6,6 26,10,10
15,15,10,6
22,6,6,6,6
14,14,6,6,6
14,10,10,6,6
10,10,10,10,6
10,6,6,6,6,6,6
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MATHEMATICA
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nn=100;
sqs=Select[Range[nn], SquareFreeQ[#]&&PrimeOmega[#]==2&];
Table[Length[IntegerPartitions[n, All, sqs]], {n, sqs}]
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CROSSREFS
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A002100 counts partitions into squarefree semiprimes.
A056768 uses primes instead of squarefree semiprimes.
A101048 counts partitions into semiprimes.
A338902 is the not necessarily squarefree version.
A339113 includes the Heinz numbers of these partitions.
A320656 counts factorizations into squarefree semiprimes.
Cf. A000041, A000607, A065516, A115392, A128301, A320655, A320732, A320892, A320912, A338915, A338916.
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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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