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A332845 a(n) = (-1)^omega(n) * Sum_{k=1..n} (-1)^omega(n/gcd(n, k)), where omega = A001221. 0
1, 0, 1, 2, 3, 0, 5, 6, 7, 0, 9, 2, 11, 0, 3, 14, 15, 0, 17, 6, 5, 0, 21, 6, 23, 0, 25, 10, 27, 0, 29, 30, 9, 0, 15, 14, 35, 0, 11, 18, 39, 0, 41, 18, 21, 0, 45, 14, 47, 0, 15, 22, 51, 0, 27, 30, 17, 0, 57, 6, 59, 0, 35, 62, 33, 0, 65, 30, 21, 0, 69, 42, 71 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..73.

FORMULA

a(n) = (-1)^omega(n) * Sum_{d|n} (-1)^omega(d) * phi(d).

a(p) = p - 2, where p is prime.

MATHEMATICA

Table[(-1)^PrimeNu[n] Sum[(-1)^PrimeNu[n/GCD[n, k]], {k, 1, n}], {n, 1, 73}]

Table[(-1)^PrimeNu[n] Sum[(-1)^PrimeNu[d] EulerPhi[d], {d, Divisors[n]}], {n, 1, 73}]

PROG

(PARI) a(n) = (-1)^omega(n) * sum(k=1, n, (-1)^omega(n/gcd(n, k))); \\ Michel Marcus, Feb 26 2020

CROSSREFS

Cf. A000010, A001221, A016825 (positions of 0's), A049060, A058026, A074722, A076479.

Sequence in context: A140700 A055615 A243059 * A190621 A325314 A322953

Adjacent sequences:  A332842 A332843 A332844 * A332846 A332847 A332848

KEYWORD

nonn,mult

AUTHOR

Ilya Gutkovskiy, Feb 26 2020

STATUS

approved

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Last modified May 9 07:57 EDT 2021. Contains 343693 sequences. (Running on oeis4.)