OFFSET
1,5
COMMENTS
A squarefree semiprime (A006881) is a product of any two distinct prime numbers.
EXAMPLE
The a(n) partitions for n = 1, 5, 7, 9, 10, 11, 13:
6 21 26 34 35 38 46
15,6 14,6,6 22,6,6 21,14 26,6,6 34,6,6
10,10,6 14,14,6 15,14,6 22,10,6 26,14,6
14,10,10 15,10,10 14,14,10 21,15,10
10,6,6,6,6 14,6,6,6,6 22,14,10
10,10,6,6,6 26,10,10
15,15,10,6
22,6,6,6,6
14,14,6,6,6
14,10,10,6,6
10,10,10,10,6
10,6,6,6,6,6,6
MATHEMATICA
nn=100;
sqs=Select[Range[nn], SquareFreeQ[#]&&PrimeOmega[#]==2&];
Table[Length[IntegerPartitions[n, All, sqs]], {n, sqs}]
CROSSREFS
A002100 counts partitions into squarefree semiprimes.
A056768 uses primes instead of squarefree semiprimes.
A101048 counts partitions into semiprimes.
A338902 is the not necessarily squarefree version.
A339113 includes the Heinz numbers of these partitions.
A320656 counts factorizations into squarefree semiprimes.
A338898/A338912/A338913 give prime indices of semiprimes, with sum/difference/product A176504/A176506/A087794.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 24 2020
STATUS
approved