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A341635
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a(n) = Sum_{d|n} phi(d) * mu(d) * mu(n/d).
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2
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1, -2, -3, 1, -5, 6, -7, 0, 2, 10, -11, -3, -13, 14, 15, 0, -17, -4, -19, -5, 21, 22, -23, 0, 4, 26, 0, -7, -29, -30, -31, 0, 33, 34, 35, 2, -37, 38, 39, 0, -41, -42, -43, -11, -10, 46, -47, 0, 6, -8, 51, -13, -53, 0, 55, 0, 57, 58, -59, 15, -61, 62, -14, 0, 65
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OFFSET
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1,2
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COMMENTS
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Abs(a(n)) <= n.
a(n) = n iff n is in A030229. (End)
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} mu(gcd(n,k)) * mu(n/gcd(n,k)).
a(1) = 1; a(n) = -Sum_{d|n, d < n} A003967(n/d) * a(d).
a(n) = Sum_{d|n} mu(n/d) * A097945(d).
Multiplicative with a(p^e) = -p if e=1, p-1 if e=2, and 0 otherwise. - Amiram Eldar, Feb 19 2021
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MATHEMATICA
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Table[Sum[EulerPhi[d] MoebiusMu[d] MoebiusMu[n/d], {d, Divisors[n]}], {n, 65}]
Table[Sum[MoebiusMu[GCD[n, k]] MoebiusMu[n/GCD[n, k]], {k, n}], {n, 65}]
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PROG
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(PARI) a(n) = sumdiv(n, d, eulerphi(d)*moebius(d)*moebius(n/d)); \\ Michel Marcus, Feb 17 2021
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CROSSREFS
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KEYWORD
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sign,mult
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AUTHOR
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STATUS
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approved
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