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

Author

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

Keywords

• nonn

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

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.

Programs

Magma

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

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&]

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