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 A089451 a(n) = mu(prime(n)-1), where mu is the Moebius function (A008683). 10
 1, -1, 0, 1, 1, 0, 0, 0, 1, 0, -1, 0, 0, -1, 1, 0, 1, 0, -1, -1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, -1, -1, 0, 0, 0, 1, 1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 0, -1, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Note that A049092 lists prime(n) such that a(n) = 0. Similarly, A078330 lists prime(n) such that a(n) = -1. See A088179 for prime(n) such that a(n) = 1. Also note that a(n) == A088144(n) (mod prime(n)). REFERENCES J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, p. 236. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Ed Pegg, Jr., Moebius Function (and squarefree numbers) Eric Weisstein's World of Mathematics, Moebius Function FORMULA a(n) = A067460(n) - 1. - Benoit Cloitre, Nov 04 2003 If p = prime(n), then a(n) is congruent modulo p to the sum of all primitive roots modulo p. [Uspensky and Heaslet]. - Michael Somos, Feb 16 2020 MATHEMATICA Table[MoebiusMu[Prime[n]-1], {n, 150}] PROG (PARI) a(n)=moebius(prime(n)-1) (MAGMA) [MoebiusMu(NthPrime(n)-1): n in [1..100]]; // Vincenzo Librandi, Dec 23 2018 CROSSREFS Cf. A089495 (mu(p+1) for prime p), A089496 (mu(p+1)+mu(p-1) for prime p), A089497 (mu(p+1)-mu(p-1) for prime p). Cf. A049092, A078330, A088144, A088179. Sequence in context: A128432 A195198 A039966 * A145099 A205083 A070886 Adjacent sequences:  A089448 A089449 A089450 * A089452 A089453 A089454 KEYWORD sign AUTHOR T. D. Noe, Nov 03 2003 STATUS approved

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Last modified April 14 07:59 EDT 2021. Contains 342946 sequences. (Running on oeis4.)