A209271 Primes p such that A066272(p)*p+1 is also prime, where A066272 is the number of anti-divisors.

5, 13, 181, 613, 761, 1201, 8581, 9661, 21013, 26681, 34061, 59513, 68821, 101701, 156241, 584281, 637321, 718801, 782501, 787513, 1078981, 1193513, 1336613, 1470613, 1529501, 1639861, 1757813, 2103301, 2257813, 2287661, 2601481, 3540461, 4307113

Offset: 1

Author

M. F. Hasler, Jan 15 2013

Keywords

• nonn

Comments

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

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.

There are only 47 such primes below 10^7.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000
• J. S. Gerasimov, Sophie Germain nonprimes [title corrected], SeqFan mailing list, Jan 15 2013

Crossrefs

Cf. A066272.

Programs

PARI

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