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A324749
Number of strict integer partitions of n containing no part > 1 whose prime indices all belong to the partition.
6
1, 1, 1, 1, 2, 1, 3, 4, 3, 4, 6, 6, 8, 11, 10, 14, 14, 19, 21, 26, 28, 35, 38, 44, 50, 60, 65, 79, 88, 98, 113, 131, 144, 165, 185, 211, 234, 268, 297, 334, 374, 420, 470, 525, 584, 649, 727, 801, 902, 998, 1100, 1220, 1357, 1500, 1657, 1833, 2029, 2220, 2462
OFFSET
0,5
COMMENTS
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.
EXAMPLE
The a(0) = 1 through a(10) = 6 strict integer partitions:
() (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
(3,1) (4,2) (4,3) (6,2) (5,4) (6,4)
(5,1) (5,2) (7,1) (6,3) (7,3)
(6,1) (7,2) (8,2)
(9,1)
(6,3,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!MemberQ[#, k_/; SubsetQ[#, PrimePi/@First/@FactorInteger[k]]]&]], {n, 0, 30}]
CROSSREFS
The subset version is A324738. The non-strict version is A324754. The Heinz number version is A324759. An infinite version is A324694.
Sequence in context: A122530 A301453 A278340 * A022466 A144254 A133310
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 15 2019
STATUS
approved