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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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Table of n, a(n) for n=1..50.
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FORMULA
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a(n) = A101048(A001358(n)).
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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.
A338903 is the squarefree version.
A339112 includes the Heinz numbers of these partitions.
A001358 lists semiprimes, with odd and even terms A046315 and A100484.
A037143 lists primes and semiprimes.
A084126 and A084127 give the prime factors of semiprimes.
A320655 counts factorizations into semiprimes.
A338898/A338912/A338913 give prime indices of semiprimes, with sum/difference/product A176504/A176506/A087794.
A338899/A270650/A270652 give prime indices of squarefree semiprimes.
Cf. A000041, A000607, A006881, A065516, A115392, A128301, A320656, A320732, A320892, A320912, A338915, A338916, A339113.
Sequence in context: A207606 A303845 A132439 * A116217 A333907 A274486
Adjacent sequences: A338899 A338900 A338901 * A338903 A338904 A338905
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Nov 24 2020
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STATUS
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approved
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