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A304362
a(n) = Sum_{d|n, d = 1 or not a perfect power} mu(n/d).
11
1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0
OFFSET
1
COMMENTS
The Moebius function mu is defined by mu(n) = (-1)^k if n is a product of k distinct primes and mu(n) = 0 otherwise.
Up to n = 10^7 this sequence only takes values in {-2, -1, 0, 1, 2}. Is this true in general?
LINKS
FORMULA
a(n) = mu(n) + Sum_{d * e = n, d in A007916, e in A005117} (-1)^omega(e), where mu = A008683 and omega = A001221.
MATHEMATICA
Table[Sum[If[GCD@@FactorInteger[d][[All, 2]]===1, MoebiusMu[n/d], 0], {d, Divisors[n]}], {n, 100}]
PROG
(PARI) A304362(n) = sumdiv(n, d, if(!ispower(d), moebius(n/d), 0)); \\ Antti Karttunen, Jul 29 2018
KEYWORD
sign
AUTHOR
Gus Wiseman, May 11 2018
EXTENSIONS
More terms from Antti Karttunen, Jul 29 2018
STATUS
approved