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

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}]

Prog

(PARI) a(n) = sumdiv(n, d, if (issquare(d), bigomega(n/d))); \\ Michel Marcus, Jun 14 2021

Crossrefs

Cf. A001222 (Omega), A345345.

Sequence in context: A257089 A328892 A296131 * A319004 A234541 A066389

Adjacent sequences: A345341 A345342 A345343 * A345345 A345346 A345347

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 14 2021

Status

approved