A209271 -id:A209271 - cp's OEIS frontend

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

Juri-Stepan Gerasimov, Jan 24 2013

nonn

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

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.

Cf. A083271, A005384, A209271, A000005.

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

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

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

A209292 Non-semiprimes n such that 2n+1 are non-semiprimes.

Original entry on oeis.org

1, 2, 3, 5, 8, 11, 13, 18, 20, 23, 29, 30, 31, 36, 37, 40, 41, 44, 48, 50, 52, 53, 54, 56, 63, 67, 68, 73, 75, 76, 78, 81, 83, 89, 90, 96, 97, 98, 99, 103, 105, 112, 113, 114, 116, 120, 125, 127, 128, 130, 131, 135, 136, 137, 138, 139, 140, 148, 153, 156

Offset: 1

Jonathan Vos Post, Jan 16 2013

This is to A005384 as nonsemiprimes A100959 are to primes A000040.

			a(1) = 1 because 1 is not a semiprime (the smallest semiprime is 4), and 2*1 + 1 = 3 is not a semiprime.
7 is not a semiprime, but 2*7 + 1 = 15 = 3*5 is a semiprime, so 7 is not in this sequence.

Cf. A001358, A005384, A100959, A209271.

SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; Select[Range[200], ! SemiPrimeQ[#] && ! SemiPrimeQ[2 # + 1] &] (* T. D. Noe, Jan 17 2013 *)

is(n)=bigomega(n)!=2 && bigomega(2*n+1)!=2 \\ Charles R Greathouse IV, Jan 16 2013

{n such that n is in A100959, and 2*n + 1 is in A100959} = {n such that n is not in A001358, and 2*n + 1 is not in A001358}.

a(n) ~ n. - Charles R Greathouse IV, Jan 16 2013

cp's OEIS Frontend

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

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