A322014 Heinz numbers of integer partitions with an even number of even parts.

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

Alois P. Heinz, Table of n, a(n) for n = 1..20000

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]]&]

Crossrefs

Cf. A000701, A046682, A056239, A058695, A058696, A108949, A296150, A321753.

Sequence in context: A325429 A004761 A004754 * A010450 A035231 A035259

Adjacent sequences: A322011 A322012 A322013 * A322015 A322016 A322017

Keyword

nonn

Author

Gus Wiseman, Nov 24 2018

Status

approved