OFFSET
1,1
COMMENTS
a(n) is of the form m^2 or 2*m^2.
(See A195268, which has similar properties.)
FORMULA
Conjecture: a(n) = 2*A023194(n). - R. J. Mathar, Sep 15 2011
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Sep 15 2011
STATUS
approved