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

%I A322014 #8 Nov 28 2018 19:02:03
%S A322014 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,
%T A322014 45,46,47,49,50,55,57,59,62,64,67,68,72,73,78,80,81,82,83,84,85,87,88,
%U A322014 90,91,92,94,97,98,99,100,103,105,109,110,111,114,115,118
%N A322014 Heinz numbers of integer partitions with an even number of even parts.
%C A322014 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A322014 Alois P. Heinz, <a href="/A322014/b322014.txt">Table of n, a(n) for n = 1..20000</a>
%p A322014 a:= proc(n) option remember; local k; for k from 1+`if`(n=1,
%p A322014       0, a(n-1)) while add(`if`(numtheory[pi](i[1])::odd,
%p A322014       0, i[2]), i=ifactors(k)[2])::odd do od; k
%p A322014     end:
%p A322014 seq(a(n), n=1..100);  # _Alois P. Heinz_, Nov 24 2018
%t A322014 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A322014 Select[Range[200],EvenQ[Count[primeMS[#],_?EvenQ]]&]
%Y A322014 Cf. A000701, A046682, A056239, A058695, A058696, A108949, A296150, A321753.
%K A322014 nonn
%O A322014 1,2
%A A322014 _Gus Wiseman_, Nov 24 2018