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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
OFFSET
1,6
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 14 2021
STATUS
approved