A209271 - OEIS

%I #16 Dec 23 2024 14:53:43

%S 5,13,181,613,761,1201,8581,9661,21013,26681,34061,59513,68821,101701,

%T 156241,584281,637321,718801,782501,787513,1078981,1193513,1336613,

%U 1470613,1529501,1639861,1757813,2103301,2257813,2287661,2601481,3540461,4307113

%N Primes p such that A066272(p)*p+1 is also prime, where A066272 is the number of anti-divisors.

%C Could be called "Sophie Germain anti-primes" or "anti-Sophie Germain primes". Inspired by the Gerasimov link.

%C Sophie Germain primes are such that 2p+1 is also prime, where 2 is the number of divisors of p. Here this is replaced with the number of anti-divisors.

%C There are only 47 such primes below 10^7.

%H Donovan Johnson, <a href="/A209271/b209271.txt">Table of n, a(n) for n = 1..1000</a>

%H J. S. Gerasimov, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-January/010687.html">Sophie Germain nonprimes</a> [title corrected], SeqFan mailing list, Jan 15 2013

%o (PARI) {forprime(n=1,default(primelimit),isprime(A066272(n)*n+1) & print1(n","))}

%Y Cf. A066272.

%K nonn

%O 1,1

%A _M. F. Hasler_, Jan 15 2013