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

Author

Gus Wiseman, Nov 24 2018

Keywords

• nonn

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

Crossrefs

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

Programs

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]]&]