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A316465 Heinz numbers of integer partitions such that every nonempty submultiset has an integer average. 1
1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 25, 27, 29, 31, 32, 34, 37, 39, 41, 43, 46, 47, 49, 53, 55, 57, 59, 61, 62, 64, 67, 68, 71, 73, 79, 81, 82, 83, 85, 87, 89, 91, 94, 97, 101, 103, 107, 109, 110, 111, 113, 115, 118, 121, 125, 127, 128 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Supersequence of A000961. - David A. Corneth, Jul 06 2018

LINKS

Table of n, a(n) for n=1..64.

EXAMPLE

Sequence of partitions begins (), (1), (2), (1,1), (3), (4), (1,1,1), (2,2), (3,1), (5), (6), (1,1,1,1), (7), (8), (4,2), (5,1), (9), (3,3), (2,2,2).

MATHEMATICA

Select[Range[100], And@@IntegerQ/@Mean/@Union[Rest[Subsets[If[#==1, {}, Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]]]]]&]

CROSSREFS

Cf. A056239, A067538, A122768, A237984, A296150, A316313, A316314, A316440, A316557.

Sequence in context: A324758 A305504 A316413 * A004764 A128649 A032894

Adjacent sequences:  A316462 A316463 A316464 * A316466 A316467 A316468

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 06 2018

STATUS

approved

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)