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A088179 Primes p such that mu(p-1) = 1; that is, p-1 is squarefree and has an even number of prime factors, where mu is the Moebius function. 8
2, 7, 11, 23, 47, 59, 83, 107, 167, 179, 211, 227, 263, 331, 347, 359, 383, 463, 467, 479, 503, 547, 563, 571, 587, 691, 719, 839, 859, 863, 887, 911, 967, 983, 1019, 1123, 1187, 1231, 1283, 1291, 1303, 1307, 1319, 1327, 1367, 1439, 1483, 1487, 1523, 1619, 1723 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It is an unsolved problem to determine if this sequence has a positive density in the primes. - Pieter Moree (moree(AT)mpim-bonn.mpg.de), Nov 03 2003

Except for the initial element 2, this sequence seems to be exactly those primes the sum of whose nonquadratic, nonprimitive-root residues is congruent to -1(mod p). - Dimitri Papadopoulos, Jan 10 2016

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Moebius Function

MAPLE

filter:= proc(p) isprime(p) and numtheory:-mobius(p-1) = 1 end proc:

select(filter, [2, seq(i, i=3..2000, 2)]); # Robert Israel, Feb 03 2016

MATHEMATICA

Select[Prime[Range[400]], MoebiusMu[ #-1]==1&]

PROG

(PARI) lista(nn) = forprime(p=2, nn, if (moebius(p-1) == 1, print1(p, ", "))); \\ Michel Marcus, Jan 10 2016

(MAGMA) [n: n in [2..2000] | IsPrime(n) and MoebiusMu(n-1) eq 1]; // Vincenzo Librandi, Jan 10 2016

CROSSREFS

Cf. A049092 (primes p with mu(p-1)=0), A078330 (primes p with mu(p-1)=-1), A089451 (mu(p-1) for prime p).

Cf. A002496.

Sequence in context: A168032 A217304 A179876 * A228434 A031873 A075356

Adjacent sequences:  A088176 A088177 A088178 * A088180 A088181 A088182

KEYWORD

nonn

AUTHOR

N. J. A. Sloane and T. D. Noe, Nov 03 2003

STATUS

approved

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Last modified December 3 01:12 EST 2016. Contains 278694 sequences.