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Sum of all integers m satisfying Omega(m) = n and pi(p) <= n for all prime factors p of m.
4

%I #18 Apr 28 2021 11:16:22

%S 1,2,19,410,14343,1139166,89131918,10861230692,1271028562739,

%T 203393524967230,52274418436233714,11160490802017899420,

%U 3415612116240107778630,1088775430914588654276060,311608007930071575510930780,99738699420765496000734958440

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

%H Alois P. Heinz, <a href="/A332967/b332967.txt">Table of n, a(n) for n = 0..279</a>

%F a(n) = [x^n] Product_{i=1..n} 1/(1-prime(i)*x).

%F a(n) = A124960(2n,n).

%F a(n) = Sum_{k=1..A088218(n)} A330394(n,k).

%F a(n) = A343751(n,n).

%e a(2) = 4 + 6 + 9 = 2*2 + 2*3 + 3*3 = 19.

%p b:= proc(n, i) option remember; `if`(n=0, 1,

%p add(ithprime(j)*b(n-1, j), j=1..i))

%p end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..17);

%Y Row sums of A330394.

%Y Main diagonal of A343751.

%Y Cf. A000040, A000720, A001222, A027748, A088218, A124960.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Mar 04 2020