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A338902
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Number of integer partitions of the n-th semiprime into semiprimes.
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7
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1, 1, 1, 2, 3, 2, 4, 7, 7, 10, 17, 25, 21, 34, 34, 73, 87, 103, 149, 176, 206, 281, 344, 479, 725, 881, 1311, 1597, 1742, 1841, 2445, 2808, 3052, 3222, 6784, 9298, 11989, 14533, 15384, 17414, 18581, 19680, 28284, 35862, 38125, 57095, 60582, 64010, 71730, 76016
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OFFSET
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1,4
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COMMENTS
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A semiprime (A001358) is a product of any two prime numbers.
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LINKS
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FORMULA
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EXAMPLE
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The a(1) = 1 through a(33) = 17 partitions of 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, where A-Z = 10-35:
4 6 9 A E F L M P Q X
64 A4 96 F6 994 FA M4 EA9
644 966 A66 L4 AA6 F99
9444 E44 A96 E66 FE4
6664 F64 9944 L66
A444 9664 A664 P44
64444 94444 E444 9996
66644 AA94
A4444 E964
644444 F666
FA44
L444
96666
A9644
F6444
966444
9444444
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MATHEMATICA
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nn=100; Table[Length[IntegerPartitions[n, All, Select[Range[nn], PrimeOmega[#]==2&]]], {n, Select[Range[nn], PrimeOmega[#]==2&]}]
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CROSSREFS
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A002100 counts partitions into squarefree semiprimes.
A056768 uses primes instead of semiprimes.
A101048 counts partitions into semiprimes.
A339112 includes the Heinz numbers of these partitions.
A037143 lists primes and semiprimes.
A320655 counts factorizations into semiprimes.
Cf. A000041, A000607, A006881, A065516, A115392, A128301, A320656, A320732, A320892, A320912, A338915, A338916, A339113.
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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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