OFFSET
0,5
FORMULA
The Heinz numbers of these partitions are given by A338316. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions.
EXAMPLE
The a(2) = 1 through a(12) = 11 partitions (A = 10, B = 11, C = 12):
2 3 4 5 6 7 8 9 A B C
22 32 33 43 44 54 55 65 66
222 52 53 72 73 74 75
322 332 333 433 83 444
2222 522 532 92 543
3222 3322 443 552
22222 533 732
722 3333
3332 5322
5222 33222
32222 222222
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !MemberQ[#, 1]&&(SameQ@@#||CoprimeQ@@Union[#])&]], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 24 2020
STATUS
approved