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%I #7 Nov 27 2020 02:06:20
%S 1,1,1,2,3,2,4,7,7,10,17,25,21,34,34,73,87,103,149,176,206,281,344,
%T 479,725,881,1311,1597,1742,1841,2445,2808,3052,3222,6784,9298,11989,
%U 14533,15384,17414,18581,19680,28284,35862,38125,57095,60582,64010,71730,76016
%N Number of integer partitions of the n-th semiprime into semiprimes.
%C A semiprime (A001358) is a product of any two prime numbers.
%F a(n) = A101048(A001358(n)).
%e 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:
%e 4 6 9 A E F L M P Q X
%e 64 A4 96 F6 994 FA M4 EA9
%e 644 966 A66 L4 AA6 F99
%e 9444 E44 A96 E66 FE4
%e 6664 F64 9944 L66
%e A444 9664 A664 P44
%e 64444 94444 E444 9996
%e 66644 AA94
%e A4444 E964
%e 644444 F666
%e FA44
%e L444
%e 96666
%e A9644
%e F6444
%e 966444
%e 9444444
%t nn=100;Table[Length[IntegerPartitions[n,All,Select[Range[nn],PrimeOmega[#]==2&]]],{n,Select[Range[nn],PrimeOmega[#]==2&]}]
%Y A002100 counts partitions into squarefree semiprimes.
%Y A056768 uses primes instead of semiprimes.
%Y A101048 counts partitions into semiprimes.
%Y A338903 is the squarefree version.
%Y A339112 includes the Heinz numbers of these partitions.
%Y A001358 lists semiprimes, with odd and even terms A046315 and A100484.
%Y A037143 lists primes and semiprimes.
%Y A084126 and A084127 give the prime factors of semiprimes.
%Y A320655 counts factorizations into semiprimes.
%Y A338898/A338912/A338913 give prime indices of semiprimes, with sum/difference/product A176504/A176506/A087794.
%Y A338899/A270650/A270652 give prime indices of squarefree semiprimes.
%Y Cf. A000041, A000607, A006881, A065516, A115392, A128301, A320656, A320732, A320892, A320912, A338915, A338916, A339113.
%K nonn
%O 1,4
%A _Gus Wiseman_, Nov 24 2020
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