A089523 - OEIS

%I #14 Sep 08 2022 08:45:12

%S 5,13,37,61,73,157,193,277,313,389,397,421,457,461,509,541,569,613,

%T 661,673,733,757,769,797,857,877,929,997,1093,1109,1153,1201,1213,

%U 1217,1229,1237,1289,1301,1321,1381,1409,1429,1453,1481,1553,1609,1621,1657

%N 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.

%H Robert Israel, <a href="/A089523/b089523.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusFunction.html">Moebius Function</a>

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

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

%o (PARI) isok(p) = isprime(p) && (moebius(p+1) == 1); \\ _Michel Marcus_, Aug 16 2018

%o (Magma) [p: p in PrimesUpTo(2000) | MoebiusMu(p+1) eq 1]; // _Vincenzo Librandi_, Aug 17 2018

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

%K nonn

%O 1,1

%A _T. D. Noe_, Nov 06 2003