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A324752
Number of strict integer partitions of n not containing 1 or any prime indices of the parts.
3
1, 0, 1, 1, 1, 1, 2, 3, 1, 4, 4, 4, 5, 6, 7, 10, 9, 12, 12, 16, 17, 22, 22, 26, 31, 35, 37, 46, 50, 55, 66, 70, 82, 90, 101, 114, 127, 143, 159, 172, 202, 215, 246, 267, 301, 327, 366, 402, 447, 491, 545, 600, 655, 722, 795, 875, 964, 1050, 1152, 1259, 1383
OFFSET
0,7
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(2) = 1 through a(17) = 12 strict integer partitions (A...H = 10...17):
2 3 4 5 6 7 8 9 A B C D E F G H
42 43 54 64 65 75 76 86 87 97 98
52 63 73 83 84 85 95 96 A6 A7
72 82 542 93 94 A4 A5 C4 B6
A2 B2 B3 B4 D3 C5
643 752 C3 E2 D4
842 D2 763 E3
654 943 854
843 A42 863
852 872
A52
B42
An example for n = 60 is (19,14,13,7,5,2), with prime indices:
19: {8}
14: {1,4}
13: {6}
7: {4}
5: {3}
2: {1}
None of these prime indices {1,3,4,6,8} belong to the partition, as required.
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!MemberQ[#, 1]&&Intersection[#, PrimePi/@First/@Join@@FactorInteger/@#]=={}&]], {n, 0, 30}]
CROSSREFS
The subset version is A324742, with maximal case is A324763. The non-strict version is A324757. The Heinz number version is A324761. An infinite version is A304360.
Sequence in context: A096180 A354265 A324336 * A298637 A034867 A323893
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 16 2019
STATUS
approved