A345345 - OEIS

A345345

a(n) = Sum_{d^2|n} omega(n/d^2).

0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 5, 1, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 5, 1, 2, 3, 3, 2, 3, 1, 3, 2, 3, 1, 6, 1, 2, 3, 3, 2, 3, 1, 5, 2, 2, 1, 5, 2, 2, 2, 4, 1, 5, 2, 3

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OFFSET

1,6

LINKS

Table of n, a(n) for n=1..92.

FORMULA

a(p) = Sum_{d^2|p} omega(p/d^2) = omega(p) = 1 for p prime.

EXAMPLE

a(12) = Sum_{d^2|12} omega(12/d^2) = omega(12) + omega(3) = 2 + 1 = 3.

MATHEMATICA

Table[Sum[PrimeNu[n/k^2] (1 - Ceiling[n/k^2] + Floor[n/k^2]), {k, n}], {n,

100}]