OFFSET
1,1
COMMENTS
If x is OPP and x=2^k*y, gcd(2^k,y)=1, (2^(k+4)+1)/3 is prime, then 4*x*(2^(k+4)+1)/3 is also OPP.
By applying the rule above to a(12) we get that 1772040615644549459607552 is also a term. - Amiram Eldar, Aug 26 2022
FORMULA
{k: A033634(k) = 2*k}.
MATHEMATICA
f[e_] := If[OddQ[e], e+2, e+1]; fun[p_, e_] := 1 + (p^f[e] - p)/(p^2 - 1); opsigma[1] = 1; opsigma[n_] := Times @@ fun @@@ FactorInteger[n]; Select[Range[50000], opsigma[#] == 2*# &] (* Amiram Eldar, Aug 26 2022 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
STATUS
approved