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A316362
Heinz numbers of strict integer partitions such that not every distinct subset has a different average.
1
30, 105, 110, 210, 238, 273, 330, 385, 390, 462, 506, 510, 546, 570, 627, 690, 714, 770, 806, 858, 870, 910, 930, 935, 966, 1001, 1110, 1131, 1155, 1190, 1230, 1254, 1290, 1326, 1330, 1365, 1394, 1410, 1430, 1482, 1495, 1518, 1590, 1729, 1770, 1785, 1786, 1794
OFFSET
1,1
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
EXAMPLE
462 is the Heinz number of (5,4,2,1), and the subsets {1,5}, and {2,4} have the same average, so 462 belongs to the sequence.
MATHEMATICA
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[3000], SquareFreeQ[#]&&!UnsameQ@@Mean/@Union[Subsets[primeMS[#]]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 30 2018
STATUS
approved