A345355 - OEIS

A345355

a(n) = Sum_{p|n, p prime} p^omega(n/p).

0, 1, 1, 2, 1, 5, 1, 2, 3, 7, 1, 7, 1, 9, 8, 2, 1, 11, 1, 9, 10, 13, 1, 7, 5, 15, 3, 11, 1, 38, 1, 2, 14, 19, 12, 13, 1, 21, 16, 9, 1, 62, 1, 15, 14, 25, 1, 7, 7, 27, 20, 17, 1, 11, 16, 11, 22, 31, 1, 42, 1, 33, 16, 2, 18, 134, 1, 21, 26, 78, 1, 13, 1, 39, 28, 23, 18, 182

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

Table of n, a(n) for n=1..78.

FORMULA

a(p) = 1 for p prime.

EXAMPLE

a(30) = Sum_{p|30} p^omega(30/p) = 2^omega(15) + 3^omega(10) + 5^omega(6) = 2^2 + 3^2 + 5^2 = 38.

MATHEMATICA

Table[Sum[k^PrimeNu[n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

PROG