A346623 a(n) = Sum_{ x <= n : x odd and omega(x) = 2 } x.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 69, 69, 104, 104, 104, 104, 143, 143, 143, 143, 143, 143, 188, 188, 188, 188, 188, 188, 239, 239, 239, 239, 294, 294, 351, 351, 351, 351, 351, 351, 414, 414, 479, 479, 479, 479

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, A346221, A346222.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+
     `if`(n::odd and nops(ifactors(n)[2])=2, n, 0))
    end:
seq(a(n), n=1..68);  # Alois P. Heinz, Aug 23 2021

Mathematica

a[n_] := a[n] = If[n == 1, 0, a[n-1] + If[OddQ[n] && PrimeNu[n] == 2, n, 0]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Feb 13 2023 *)

Python

from sympy import primefactors
def A346623(n):
    return 0 if n <= 2 else A346623(n-1) + (n if n % 2 and len(primefactors(n)) == 2 else 0) # Chai Wah Wu, Aug 23 2021