A195334 Numbers the sum of whose even divisors is 2 times a prime.

4, 8, 18, 32, 50, 128, 578, 1458, 3362, 4802, 6962, 8192, 10082, 15842, 20402, 31250, 34322, 55778, 57122, 59858, 131072, 167042, 171698, 293378, 524288, 559682, 916658, 982802, 1062882, 1104098, 1158242, 1195058, 1367858, 1407842, 1414562, 1468898, 1659842

Offset: 1

Author

Michel Lagneau, Sep 15 2011

Keywords

• nonn

Comments

a(n) is of the form m^2 or 2*m^2.

(See A195268, which has similar properties.)

Examples

			The divisors of 18 are {1, 2, 3, 6, 9, 18}, and half the sum of the even divisors is (2 + 6 + 18)/2 = 26/2 = 13, which is prime. Hence 18 is in the sequence.
		

Crossrefs

Cf. A146076, A195268.

Programs

Maple

A146076 := proc(n) a :=0 ; for d in numtheory[divisors](n) do if type(d,'even') then a := a+d; end if; end do; a; end proc:
isA195334 := proc(n) isprime(A146076(n)/2) ; end proc:
for n from 1 do if isA195334(n) then print(n); end if; end do: # R. J. Mathar, Sep 15 2011

Mathematica

Select[Range[2000000],PrimeQ[Total[Select[Divisors[#],EvenQ]]/2]&] (* Harvey P. Dale, Mar 07 2012 *)

Formula

Conjecture: a(n) = 2*A023194(n). - R. J. Mathar, Sep 15 2011