A316465 Heinz numbers of integer partitions such that every nonempty submultiset has an integer average.

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

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: A316413 A360009 A359905 * A004764 A128649 A032894

Adjacent sequences: A316462 A316463 A316464 * A316466 A316467 A316468

Keyword

nonn

Author

Gus Wiseman, Jul 06 2018

Status

approved