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%I #14 Feb 27 2024 14:28:45
%S 1,1,2,4,6,12,22,44,56,76,130,260,376,752,1248,1948,2224,4448,5808,
%T 11616,16016,24000,38416,76832,94656,114736,181992,204024,274056,
%U 548112,743856,1487712,1593696,2292992,3590880,4881120,5630592,11261184,17559072,24987360
%N Number of ways to choose a subset s of [n] and then for each element in s choose a different prime factor.
%H Alois P. Heinz, <a href="/A370648/b370648.txt">Table of n, a(n) for n = 0..140</a>
%F a(p) = 2 * a(p-1) for prime p.
%p b:= proc(n, s) option remember; uses numtheory; `if`(n=0, 1, b(n-1, s)+
%p add(b(n-1, select(x-> x<n, s union {j})), j=factorset(n) minus s))
%p end:
%p a:= n-> b(n, {}):
%p seq(a(n), n=0..42);
%Y Cf. A000040, A370582.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Feb 25 2024