A346621 a(n) = Sum_{ x <= n : omega(x) = 2 } x.

0, 0, 0, 0, 0, 6, 6, 6, 6, 16, 16, 28, 28, 42, 57, 57, 57, 75, 75, 95, 116, 138, 138, 162, 162, 188, 188, 216, 216, 216, 216, 216, 249, 283, 318, 354, 354, 392, 431, 471, 471, 471, 471, 515, 560, 606, 606, 654, 654, 704, 755, 807, 807, 861, 916, 972, 1029, 1087, 1087, 1087

Offset: 1

Author

N. J. A. Sloane, Aug 23 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A001221, A007774, A082997, A346622, A346623.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 0,
      a(n-1)+`if`(nops(ifactors(n)[2])=2, n, 0))
    end:
seq(a(n), n=1..60);  # Alois P. Heinz, Aug 23 2021

Mathematica

a[n_] := a[n] = If[n <= 2, 0, a[n-1] + If[PrimeNu[n] == 2, n, 0]];
Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Apr 24 2025 *)

PARI

a(n) = sum(x=1, n, if (omega(x)==2, x)); \\ Michel Marcus, Aug 23 2021

Python

from sympy import primefactors
def A346621(n):
    return 0 if n <= 2 else A346621(n-1) + (n if len(primefactors(n)) == 2 else 0) # Chai Wah Wu, Aug 23 2021