A345344 - OEIS

A345344

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

0, 1, 1, 2, 1, 2, 1, 4, 2, 2, 1, 4, 1, 2, 2, 6, 1, 4, 1, 4, 2, 2, 1, 6, 2, 2, 4, 4, 1, 3, 1, 9, 2, 2, 2, 8, 1, 2, 2, 6, 1, 3, 1, 4, 4, 2, 1, 9, 2, 4, 2, 4, 1, 6, 2, 6, 2, 2, 1, 6, 1, 2, 4, 12, 2, 3, 1, 4, 2, 3, 1, 12, 1, 2, 4, 4, 2, 3, 1, 9, 6, 2, 1, 6, 2, 2, 2, 6, 1, 6, 2, 4, 2

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OFFSET

1,4

LINKS

Table of n, a(n) for n=1..93.

FORMULA

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

EXAMPLE

a(24) = Sum_{d^2|24} Omega(24/d^2) = Omega(24) + Omega(6) = 4 + 2 = 6.

a(32) = Sum_{d^2|32} Omega(32/d^2) = Omega(32) + Omega(8) + Omega(2) = 5 + 3 + 1 = 9.

MATHEMATICA

Table[Sum[PrimeOmega[n/k^2] (1 - Ceiling[n/k^2] + Floor[n/k^2]), {k, n}], {n, 100}]