A089523 Primes p such that mu(p+1) = 1; that is, p+1 is squarefree and has an even number of distinct prime factors, where mu is the Moebius function.

5, 13, 37, 61, 73, 157, 193, 277, 313, 389, 397, 421, 457, 461, 509, 541, 569, 613, 661, 673, 733, 757, 769, 797, 857, 877, 929, 997, 1093, 1109, 1153, 1201, 1213, 1217, 1229, 1237, 1289, 1301, 1321, 1381, 1409, 1429, 1453, 1481, 1553, 1609, 1621, 1657

Offset: 1

Author

T. D. Noe, Nov 06 2003

Keywords

• nonn

Links

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

Crossrefs

Cf. A089495 (mu(p+1) for prime p), A049098 (primes p with mu(p+1)=0), A078329 (primes p with mu(p+1)=-1).

Programs

Magma

[p: p in PrimesUpTo(2000) | MoebiusMu(p+1) eq 1]; // Vincenzo Librandi, Aug 17 2018

Maple

select(n -> isprime(n) and numtheory:-mobius(n+1)=1, [seq(i,i=1..2000,4)]); # Robert Israel, Aug 16 2018

Mathematica

Select[Prime[Range[300]], MoebiusMu[ #+1]==1&]

PARI

isok(p) = isprime(p) && (moebius(p+1) == 1); \\ Michel Marcus, Aug 16 2018