

A088179


Primes p such that mu(p1) = 1; that is, p1 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
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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)mpimbonn.mpg.de), Nov 03 2003
Except for the initial element 2, this sequence seems to be exactly those primes the sum of whose nonquadratic, nonprimitiveroot 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(p1) = 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(p1) == 1, print1(p, ", "))); \\ Michel Marcus, Jan 10 2016
(MAGMA) [n: n in [2..2000]  IsPrime(n) and MoebiusMu(n1) eq 1]; // Vincenzo Librandi, Jan 10 2016


CROSSREFS

Cf. A049092 (primes p with mu(p1)=0), A078330 (primes p with mu(p1)=1), A089451 (mu(p1) 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



