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A322014
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Heinz numbers of integer partitions with an even number of even parts.
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1
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1, 2, 4, 5, 8, 9, 10, 11, 16, 17, 18, 20, 21, 22, 23, 25, 31, 32, 34, 36, 39, 40, 41, 42, 44, 45, 46, 47, 49, 50, 55, 57, 59, 62, 64, 67, 68, 72, 73, 78, 80, 81, 82, 83, 84, 85, 87, 88, 90, 91, 92, 94, 97, 98, 99, 100, 103, 105, 109, 110, 111, 114, 115, 118
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OFFSET
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1,2
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COMMENTS
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The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
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LINKS
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MAPLE
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a:= proc(n) option remember; local k; for k from 1+`if`(n=1,
0, a(n-1)) while add(`if`(numtheory[pi](i[1])::odd,
0, i[2]), i=ifactors(k)[2])::odd do od; k
end:
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[200], EvenQ[Count[primeMS[#], _?EvenQ]]&]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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