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A345345 a(n) = Sum_{d^2|n} omega(n/d^2). 1
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 (list; graph; refs; listen; history; text; internal format)
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}]

PROG

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

CROSSREFS

Cf. A001221 (omega), A062799, A345344.

Sequence in context: A341596 A099042 A140774 * A056924 A342083 A316364

Adjacent sequences:  A345342 A345343 A345344 * A345346 A345348 A345349

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jun 14 2021

STATUS

approved

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Last modified November 27 09:19 EST 2021. Contains 349365 sequences. (Running on oeis4.)