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Number of strict integer partitions of n not containing 1 or any part whose prime indices all belong to the partition.
8

%I #7 Mar 16 2019 10:12:33

%S 1,0,1,1,1,1,2,3,2,4,4,4,6,8,8,11,10,15,16,19,23,27,28,35,39,47,50,63,

%T 68,77,91,102,114,130,147,169,187,213,237,268,300,336,380,422,472,525,

%U 587,647,731,810,895,996,1102,1227,1355,1498,1661,1818,2020,2221

%N Number of strict integer partitions of n not containing 1 or any part whose prime indices all belong to the partition.

%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

%e The a(2) = 1 through a(17) = 15 strict integer partitions (A...H = 10...17):

%e 2 3 4 5 6 7 8 9 A B C D E F G H

%e 42 43 62 54 64 65 75 76 86 87 97 98

%e 52 63 73 83 84 85 95 96 A6 A7

%e 72 82 542 93 94 A4 A5 C4 B6

%e A2 A3 B3 B4 D3 C5

%e 642 B2 C2 C3 E2 D4

%e 643 752 D2 763 E3

%e 652 842 654 862 F2

%e 762 943 854

%e 843 A42 863

%e 852 872

%e A43

%e A52

%e B42

%e 6542

%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&!MemberQ[#,1]&&!MemberQ[#,k_/;SubsetQ[#,PrimePi/@First/@FactorInteger[k]]]&]],{n,0,30}]

%Y The subset version is A324739. The non-strict version is A324755. The Heinz number version is A324760. An infinite version is A324694.

%Y Cf. A000720, A001462, A007097, A074971, A078374, A112798, A276625, A290822, A304360, A305713, A306844.

%Y Cf. A324696, A324737, A324742, A324744, A324764.

%K nonn

%O 0,7

%A _Gus Wiseman_, Mar 15 2019