A325761 - OEIS

A325761

Heinz numbers of integer partitions whose length is itself a part.

1, 2, 6, 9, 15, 20, 21, 30, 33, 39, 45, 50, 51, 56, 57, 69, 70, 75, 84, 87, 93, 105, 110, 111, 123, 125, 126, 129, 130, 140, 141, 159, 165, 170, 175, 176, 177, 183, 189, 190, 195, 196, 201, 210, 213, 219, 230, 237, 245, 249, 255, 264, 267, 275, 285, 290, 291

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OFFSET

1,2

COMMENTS

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

The enumeration of these partitions by sum is given by A002865.

LINKS

Table of n, a(n) for n=1..57.

EXAMPLE

The sequence of terms together with their prime indices begins:

1: {}

2: {1}

6: {1,2}

9: {2,2}

15: {2,3}

20: {1,1,3}

21: {2,4}

30: {1,2,3}

33: {2,5}

39: {2,6}

45: {2,2,3}

50: {1,3,3}

51: {2,7}

56: {1,1,1,4}

57: {2,8}

69: {2,9}

70: {1,3,4}

75: {2,3,3}

84: {1,1,2,4}

87: {2,10}

MATHEMATICA

Select[Range[100], MemberQ[PrimePi/@First/@FactorInteger[#], PrimeOmega[#]]&]

CROSSREFS

Cf. A001222, A002865, A056239, A093641, A109298, A110295, A112798, A118914, A325762, A325763.

Sequence in context: A353083 A049634 A120387 * A176039 A260699 A084265

Adjacent sequences: A325758 A325759 A325760 * A325762 A325763 A325764

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 18 2019

STATUS

approved