A089451 - OEIS

A089451

a(n) = mu(prime(n)-1), where mu is the Moebius function (A008683).

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

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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 A374045 A205083

Adjacent sequences: A089448 A089449 A089450 * A089452 A089453 A089454

KEYWORD

sign

AUTHOR

T. D. Noe, Nov 03 2003

STATUS

approved