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A049092
Primes p such that p-1 is not squarefree.
7
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved