This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A252541 #29 May 19 2024 02:14:46
%S A252541 6,14,62,254,756,16382,262142,1048574,39606840,4294967294
%N A252541 Numbers k such that A146076(A000593(k)) = k.
%C A252541 All integers of the form 2*(2^p-1) where 2^p-1 is prime are terms (see A139257). The terms that are not of this form are 756, 39606840. Are there any other? [Edited by _Michel Marcus_, Nov 22 2022]
%C A252541 All terms are even because all terms of A146076 are even. - _Michel Marcus_, Nov 22 2022
%C A252541 a(11) > 10^10. - _Michel Marcus_, Nov 22 2022
%C A252541 a(11) > 10^11. - _Amiram Eldar_, May 19 2024
%e A252541 14 is in the sequence because the divisors are {1, 2, 7, 14} => sum of odd divisors 1 + 7 = 8. The divisors of 8 are {1, 2, 4, 8} => sum of even divisors = 2 + 4 + 8 = 14. That is, A146076(A000593(14)) = A146076(8) = 14.
%t A252541 f[n_]:= Plus @@ Select[ Divisors@ n, OddQ];g[n_]:= Plus @@ Select[ Divisors@ n, EvenQ];Do[If[g[f[n]]==n,Print[n]],{n,1,10^8}]
%o A252541 (PARI) sod(n) = sigma(n>>valuation(n, 2)); \\ A000593
%o A252541 sed(n) = if (n%2, 0, 2*sigma(n/2)); \\ A146076
%o A252541 isok(n) = sed(sod(n)) == n;
%o A252541 lista(nn) = forstep(n=2, nn, 2, if(isok(n), print1(n, ", "))); \\ _Michel Marcus_, Nov 22 2022
%Y A252541 Cf. A000593 (sum of odd divisors), A139257, A146076 (sum of even divisors), A252540.
%K A252541 nonn,more
%O A252541 1,1
%A A252541 _Michel Lagneau_, Dec 18 2014
%E A252541 a(10) from _Michel Marcus_, Nov 22 2022