The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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 Antti Karttunen, Table of n, a(n) for n = 1..65537 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 CROSSREFS Cf. A000005, A000961, A001221, A001597, A001694, A005117, A007916, A008683, A091050, A203025, A304326, A304327, A304364, A304365, A304369. Sequence in context: A227291 A271102 A326072 * A330682 A230135 A205633 Adjacent sequences:  A304359 A304360 A304361 * A304363 A304364 A304365 KEYWORD sign AUTHOR Gus Wiseman, May 11 2018 EXTENSIONS More terms from Antti Karttunen, Jul 29 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 23 15:34 EST 2020. Contains 332167 sequences. (Running on oeis4.)