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

1, 2, 19, 410, 14343, 1139166, 89131918, 10861230692, 1271028562739, 203393524967230, 52274418436233714, 11160490802017899420, 3415612116240107778630, 1088775430914588654276060, 311608007930071575510930780, 99738699420765496000734958440

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..279

Formula

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

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

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

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

Example

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

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
      add(ithprime(j)*b(n-1, j), j=1..i))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..17);

Crossrefs

Row sums of A330394.

Main diagonal of A343751.

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

Sequence in context: A378042 A379897 A353290 * A120420 A350939 A239674

Adjacent sequences: A332964 A332965 A332966 * A332968 A332969 A332970

Keyword

nonn

Author

Alois P. Heinz, Mar 04 2020

Status

approved