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

1,2

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.

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 *)

Prog

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

Crossrefs

Cf. A083271, A005384, A209271, A000005.

Sequence in context: A047596 A199502 A089964 * A179302 A240083 A066996

Adjacent sequences: A210492 A210493 A210494 * A210496 A210497 A210498

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 24 2013

Status

approved