A324759 - OEIS

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A324759

Heinz numbers of integer partitions containing no part > 1 whose prime indices all belong to the partition.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 39, 40, 41, 43, 44, 46, 47, 49, 50, 51, 52, 53, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 71, 73, 74, 77, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93

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OFFSET

1,2

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. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

LINKS

Table of n, a(n) for n=1..67.

EXAMPLE

The sequence of terms together with their prime indices begins:

1: {}

2: {1}

3: {2}

4: {1,1}

5: {3}

7: {4}

8: {1,1,1}

9: {2,2}

10: {1,3}

11: {5}

13: {6}

16: {1,1,1,1}

17: {7}

19: {8}

20: {1,1,3}

21: {2,4}

22: {1,5}

23: {9}

25: {3,3}

26: {1,6}

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

Select[Range[100], !MemberQ[DeleteCases[primeMS[#], 1], k_/; SubsetQ[primeMS[#], primeMS[k]]]&]

CROSSREFS

The subset version is A324738, with maximal case A324744. The strict integer partition version is A324749. The integer partition version is A324754. An infinite version is A324694.

Cf. A000720, A001221, A007097, A056239, A112798, A276625, A289509, A290822, A306844, A324695, A324750, A324755, A324760.

Sequence in context: A218444 A325118 A014122 * A360550 A326621 A324758

Adjacent sequences: A324756 A324757 A324758 * A324760 A324761 A324762

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 17 2019

STATUS

approved