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A332845 a(n) = (-1)^omega(n) * Sum_{k=1..n} (-1)^omega(n/gcd(n, k)), where omega = A001221. 0

%I

%S 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,

%T 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,

%U 30,17,0,57,6,59,0,35,62,33,0,65,30,21,0,69,42,71

%N a(n) = (-1)^omega(n) * Sum_{k=1..n} (-1)^omega(n/gcd(n, k)), where omega = A001221.

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

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

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

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

%o (PARI) a(n) = (-1)^omega(n) * sum(k=1, n, (-1)^omega(n/gcd(n, k))); \\ _Michel Marcus_, Feb 26 2020

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

%K nonn,mult

%O 1,4

%A _Ilya Gutkovskiy_, Feb 26 2020

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Last modified June 19 15:52 EDT 2021. Contains 345143 sequences. (Running on oeis4.)