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A089451
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a(n) = mu(prime(n)-1), where mu is the Moebius function (A008683).
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10
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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
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1,1
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COMMENTS
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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)).
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REFERENCES
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J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, p. 236.
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LINKS
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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
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FORMULA
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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
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MATHEMATICA
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Table[MoebiusMu[Prime[n]-1], {n, 150}]
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PROG
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(PARI) a(n)=moebius(prime(n)-1)
(MAGMA) [MoebiusMu(NthPrime(n)-1): n in [1..100]]; // Vincenzo Librandi, Dec 23 2018
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CROSSREFS
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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
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KEYWORD
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sign
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AUTHOR
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T. D. Noe, Nov 03 2003
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STATUS
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approved
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