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A332967 Sum of all integers m satisfying Omega(m) = n and pi(p) <= n for all prime factors p of m.

%I A332967 #18 Apr 28 2021 11:16:22
%S A332967 1,2,19,410,14343,1139166,89131918,10861230692,1271028562739,
%T A332967 203393524967230,52274418436233714,11160490802017899420,
%U A332967 3415612116240107778630,1088775430914588654276060,311608007930071575510930780,99738699420765496000734958440
%N A332967 Sum of all integers m satisfying Omega(m) = n and pi(p) <= n for all prime factors p of m.
%H A332967 Alois P. Heinz, <a href="/A332967/b332967.txt">Table of n, a(n) for n = 0..279</a>
%F A332967 a(n) = [x^n] Product_{i=1..n} 1/(1-prime(i)*x).
%F A332967 a(n) = A124960(2n,n).
%F A332967 a(n) = Sum_{k=1..A088218(n)} A330394(n,k).
%F A332967 a(n) = A343751(n,n).
%e A332967 a(2) = 4 + 6 + 9 = 2*2 + 2*3 + 3*3 = 19.
%p A332967 b:= proc(n, i) option remember; `if`(n=0, 1,
%p A332967       add(ithprime(j)*b(n-1, j), j=1..i))
%p A332967     end:
%p A332967 a:= n-> b(n$2):
%p A332967 seq(a(n), n=0..17);
%Y A332967 Row sums of A330394.
%Y A332967 Main diagonal of A343751.
%Y A332967 Cf. A000040, A000720, A001222, A027748, A088218, A124960.
%K A332967 nonn
%O A332967 0,2
%A A332967 _Alois P. Heinz_, Mar 04 2020