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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..48.

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[#]]]&]

CROSSREFS

Cf. A032302, A056239, A108917, A122768, A275972, A276024, A296150, A299702, A301899, A316313, A316314, A316361.

Sequence in context: A039395 A043998 A101056 * A081370 A257891 A158445

Adjacent sequences:  A316359 A316360 A316361 * A316363 A316364 A316365

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 30 2018

STATUS

approved

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Last modified March 24 11:34 EDT 2019. Contains 321448 sequences. (Running on oeis4.)