A210495 Numbers n such that d(n)*n + 1 is prime, d(n) = number of divisors of n.

1, 2, 3, 4, 5, 10, 11, 12, 15, 18, 22, 23, 24, 27, 29, 30, 32, 34, 39, 41, 42, 45, 52, 53, 54, 56, 57, 58, 63, 64, 68, 69, 76, 83, 84, 87, 89, 93, 96, 108, 110, 113, 115, 131, 142, 144, 147, 150, 152, 153, 156, 162, 165, 168, 170, 172, 173, 175, 177

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 24 2013

Keywords

• nonn

Comments

This is the union of Sophie Germain primes and Sophie Germain nonprimes, so it might be called "Sophie Germain numbers".

Links

• Harvey P. Dale, 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. A083271, A005384, A209271, A000005.

Programs

Maple

A210495 := proc(n)
    option remember;
    local a;
    if n = 1 then
        1 ;
    else
        for a from procname(n-1)+1 do
            if isprime(numtheory[tau](a)*a+1) then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Jan 27 2013

Mathematica

Select[Range[200],PrimeQ[# DivisorSigma[0,#]+1]&] (* Harvey P. Dale, Aug 26 2013 *)

PARI

is(n)=isprime(numdiv(n)*n+1) \\ Charles R Greathouse IV, Jan 24 2013