cp's OEIS Frontend

A338902 Number of integer partitions of the n-th semiprime into semiprimes.

%I A338902 #7 Nov 27 2020 02:06:20
%S A338902 1,1,1,2,3,2,4,7,7,10,17,25,21,34,34,73,87,103,149,176,206,281,344,
%T A338902 479,725,881,1311,1597,1742,1841,2445,2808,3052,3222,6784,9298,11989,
%U A338902 14533,15384,17414,18581,19680,28284,35862,38125,57095,60582,64010,71730,76016
%N A338902 Number of integer partitions of the n-th semiprime into semiprimes.
%C A338902 A semiprime (A001358) is a product of any two prime numbers.
%F A338902 a(n) = A101048(A001358(n)).
%e A338902 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 A338902   4  6  9  A   E    F   L     M      P      Q       X
%e A338902            64  A4   96  F6    994    FA     M4      EA9
%e A338902                644      966   A66    L4     AA6     F99
%e A338902                         9444  E44    A96    E66     FE4
%e A338902                               6664   F64    9944    L66
%e A338902                               A444   9664   A664    P44
%e A338902                               64444  94444  E444    9996
%e A338902                                             66644   AA94
%e A338902                                             A4444   E964
%e A338902                                             644444  F666
%e A338902                                                     FA44
%e A338902                                                     L444
%e A338902                                                     96666
%e A338902                                                     A9644
%e A338902                                                     F6444
%e A338902                                                     966444
%e A338902                                                     9444444
%t A338902 nn=100;Table[Length[IntegerPartitions[n,All,Select[Range[nn],PrimeOmega[#]==2&]]],{n,Select[Range[nn],PrimeOmega[#]==2&]}]
%Y A338902 A002100 counts partitions into squarefree semiprimes.
%Y A338902 A056768 uses primes instead of semiprimes.
%Y A338902 A101048 counts partitions into semiprimes.
%Y A338902 A338903 is the squarefree version.
%Y A338902 A339112 includes the Heinz numbers of these partitions.
%Y A338902 A001358 lists semiprimes, with odd and even terms A046315 and A100484.
%Y A338902 A037143 lists primes and semiprimes.
%Y A338902 A084126 and A084127 give the prime factors of semiprimes.
%Y A338902 A320655 counts factorizations into semiprimes.
%Y A338902 A338898/A338912/A338913 give prime indices of semiprimes, with sum/difference/product A176504/A176506/A087794.
%Y A338902 A338899/A270650/A270652 give prime indices of squarefree semiprimes.
%Y A338902 Cf. A000041, A000607, A006881, A065516, A115392, A128301, A320656, A320732, A320892, A320912, A338915, A338916, A339113.
%K A338902 nonn
%O A338902 1,4
%A A338902 _Gus Wiseman_, Nov 24 2020