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A322014
Heinz numbers of integer partitions with an even number of even parts.
1
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
OFFSET
1,2
COMMENTS
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
LINKS
MAPLE
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:
seq(a(n), n=1..100); # Alois P. Heinz, Nov 24 2018
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[200], EvenQ[Count[primeMS[#], _?EvenQ]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 24 2018
STATUS
approved