cp's OEIS Frontend

A370648 Number of ways to choose a subset s of [n] and then for each element in s choose a different prime factor.

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