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A324753
Number of integer partitions of n containing all prime indices of their parts.
16
1, 1, 1, 2, 2, 4, 5, 7, 8, 14, 16, 23, 29, 40, 49, 66, 81, 109, 133, 172, 211, 274, 332, 419, 511, 640, 775, 965, 1165, 1434, 1730, 2109, 2530, 3083, 3683, 4447, 5308, 6375, 7573, 9062, 10730, 12786, 15104, 17909, 21095, 24937, 29284, 34488, 40421, 47450
OFFSET
0,4
COMMENTS
These could be described as transitive integer partitions.
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(1) = 1 through a(8) = 8 integer partitions:
(1) (11) (21) (211) (41) (321) (421) (3221)
(111) (1111) (221) (411) (2221) (4211)
(2111) (2211) (3211) (22211)
(11111) (21111) (4111) (32111)
(111111) (22111) (41111)
(211111) (221111)
(1111111) (2111111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], SubsetQ[#, PrimePi/@First/@Join@@FactorInteger/@DeleteCases[#, 1]]&]], {n, 0, 30}]
CROSSREFS
The subset version is A324736. The strict case is A324748. The Heinz number version is A290822. An infinite version is A324698.
Sequence in context: A348552 A058678 A241410 * A374020 A283106 A030769
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 16 2019
STATUS
approved