A049092 Primes p such that p-1 is not squarefree.

5, 13, 17, 19, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 127, 137, 149, 151, 157, 163, 173, 181, 193, 197, 199, 229, 233, 241, 251, 257, 269, 271, 277, 281, 293, 307, 313, 317, 337, 349, 353, 373, 379, 389, 397, 401, 409, 421, 433, 449, 457, 461, 487

Offset

1,1

Comments

Primes p with mu(p-1)=0, where mu is the Möbius function. - T. D. Noe, Nov 03 2003

Primes p such that the sum of the primitive roots of p (see A088144) is 0 mod p. - Jon Wharf, Mar 12 2015

The relative density of this sequence within the primes is 1 - A005596 = 0.626044... - Amiram Eldar, Feb 10 2021

Links

T. D. Noe, Table of n, a(n) for n=1..1000

Eric Weisstein's World of Mathematics, Moebius Function.

Formula

a(n) = A145199(n) + 1. - Amiram Eldar, Feb 10 2021

Example

p = 257 is here because p-1 = 256 = 2^8.
p = 997 is here because p-1 = 996 = 3*(2^2)*83.

Mathematica

Select[Prime[Range[400]], MoebiusMu[ #-1]==0&]

Prog

(Magma) [ p: p in PrimesUpTo(500) | not IsSquarefree(p-1) ]; // Vincenzo Librandi, Mar 12 2015
(PARI) forprime(p=2, 500, if(!issquarefree(p-1), print(p))) \\ Michael B. Porter, Mar 16 2015

Crossrefs

Cf. A005596, A039787, A078330 (primes p with mu(p-1)=-1), A088179 (primes p such that mu(p-1)=1), A089451 (mu(p-1) for prime p), A145199.

Sequence in context: A088908 A327638 A092218 * A103666 A082700 A212287

Adjacent sequences: A049089 A049090 A049091 * A049093 A049094 A049095

Keyword

nonn

Author

Labos Elemer

Status

approved