cp's OEIS Frontend

A338903 Number of integer partitions of the n-th squarefree semiprime into squarefree semiprimes.

%I A338903 #6 Nov 27 2020 02:06:32
%S A338903 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,
%T A338903 163,207,233,259,260,514,657,813,983,1010,1215,1255,1720,2112,2256,
%U A338903 3171,3370,3499,3864,4103,6292,7313,7620,8374,10650,17579,18462,23034,25180
%N A338903 Number of integer partitions of the n-th squarefree semiprime into squarefree semiprimes.
%C A338903 A squarefree semiprime (A006881) is a product of any two distinct prime numbers.
%F A338903 a(n) = A002100(A006881(n)).
%e A338903 The a(n) partitions for n = 1, 5, 7, 9, 10, 11, 13:
%e A338903   6  21    26       34          35        38           46
%e A338903      15,6  14,6,6   22,6,6      21,14     26,6,6       34,6,6
%e A338903            10,10,6  14,14,6     15,14,6   22,10,6      26,14,6
%e A338903                     14,10,10    15,10,10  14,14,10     21,15,10
%e A338903                     10,6,6,6,6            14,6,6,6,6   22,14,10
%e A338903                                           10,10,6,6,6  26,10,10
%e A338903                                                        15,15,10,6
%e A338903                                                        22,6,6,6,6
%e A338903                                                        14,14,6,6,6
%e A338903                                                        14,10,10,6,6
%e A338903                                                        10,10,10,10,6
%e A338903                                                        10,6,6,6,6,6,6
%t A338903 nn=100;
%t A338903 sqs=Select[Range[nn],SquareFreeQ[#]&&PrimeOmega[#]==2&];
%t A338903 Table[Length[IntegerPartitions[n,All,sqs]],{n,sqs}]
%Y A338903 A002100 counts partitions into squarefree semiprimes.
%Y A338903 A056768 uses primes instead of squarefree semiprimes.
%Y A338903 A101048 counts partitions into semiprimes.
%Y A338903 A338902 is the not necessarily squarefree version.
%Y A338903 A339113 includes the Heinz numbers of these partitions.
%Y A338903 A001358 lists semiprimes, with odd and even terms A046315 and A100484.
%Y A338903 A006881 lists squarefree semiprimes, with odd and even terms A046388 and A100484.
%Y A338903 A320656 counts factorizations into squarefree semiprimes.
%Y A338903 A338898/A338912/A338913 give prime indices of semiprimes, with sum/difference/product A176504/A176506/A087794.
%Y A338903 A338899, A270650, and A270652 give the prime indices of squarefree semiprimes.
%Y A338903 Cf. A000041, A000607, A065516, A115392, A128301, A320655, A320732, A320892, A320912, A338915, A338916.
%K A338903 nonn
%O A338903 1,5
%A A338903 _Gus Wiseman_, Nov 24 2020