OFFSET
1,1
FORMULA
Solutions x to sigma[n]-2n=x where Abs[x] is a prime number.
EXAMPLE
n=18: sigma[18]=18+9+6+3+2+1=39, 2n=36, abundance=3, a prime;
n=25: sigma[25]=25+5+1=31, 2n=50, abundance=-19.
MATHEMATICA
ab[x_] := DivisorSigma[1, x]-2*x Do[If[PrimeQ[s=ab[n]], Print[s]], {n, 1, 10000}]
Select[Table[DivisorSigma[1, n]-2n, {n, 7000}], PrimeQ[Abs[#]]&] (* Harvey P. Dale, Aug 21 2011 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Labos Elemer, Oct 18 2003
STATUS
approved