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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
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
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}]]]]]]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 06 2018
STATUS
approved