# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a033289
Showing 1-1 of 1

%I A033289 #15 Aug 26 2022 07:28:58
%S A033289 6,264,45408,10177920,9310826880,27806077440,25437179036160,
%T A033289 303753589954560,277875743791011840,14504815632384,13269098919960576,
%U A033289 2534919599177957376,2318960803647990104064
%N A033289 Odd power perfect numbers: numbers k such that opsigma(k) = 2*k, where opsigma(k) = A033634(k).
%C A033289 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.
%C A033289 By applying the rule above to a(12) we get that 1772040615644549459607552 is also a term. - _Amiram Eldar_, Aug 26 2022
%F A033289 {k: A033634(k) = 2*k}.
%t A033289 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 *)
%Y A033289 Cf. A000978, A033634.
%K A033289 nonn,more
%O A033289 1,1
%A A033289 _Yasutoshi Kohmoto_

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE