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.

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

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
(PARI) list(lim)=my(v=List(), last); forsquarefree(k=1, lim\1, if(moebius(k)==1, last=k[1], if(k[2][, 2]==[1]~ && k[1]-last==1, listput(v, k[1])))); Vec(v) \\ Charles R Greathouse IV, Jan 08 2018
(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: A329309 A217304 A179876 * A362629 A228434 A031873

Adjacent sequences: A088176 A088177 A088178 * A088180 A088181 A088182

Keyword

nonn

Author

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

Status

approved