A078330 Primes p such that mu(p-1) = -1, where mu is the Moebius function; that is, p-1 is squarefree and has an odd number of prime factors.

3, 31, 43, 67, 71, 79, 103, 131, 139, 191, 223, 239, 283, 311, 367, 419, 431, 439, 443, 499, 599, 607, 619, 643, 647, 659, 683, 743, 787, 823, 827, 907, 947, 971, 1031, 1039, 1087, 1091, 1103, 1163, 1223, 1259, 1399, 1427, 1447, 1499, 1511, 1543, 1559, 1571

Offset: 1

Author

Shyam Sunder Gupta, Nov 21 2002

Keywords

• easy
• nonn

Examples

			31 is in the sequence because 31 is a prime and mu(30) = -1.
37 is not in the sequence because, although 37 is prime, mu(36) = 0.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Moebius Function.

Crossrefs

Cf. A008683, A049092 (primes p with mu(p-1) = 0), A088179 (primes p with mu(p-1) = 1), A089451 (mu(p-1) for prime p).

Programs

Mathematica

Select[Prime[Range[400]], MoebiusMu[# - 1] == -1 &] (* from T. D. Noe *)

PARI

j=[]; forprime(n=1,2000,if(moebius(n)==moebius(n-1),j=concat(j,n))); j