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 A066175 #21 May 15 2023 14:27:28 %S A066175 1,3,7,15,31,127,1023,8191,131071,524287,2147483647 %N A066175 Numbers k such that sigma(phi(sigma(k))) = k. %C A066175 If n=2^k-1, where either k=1, or n is a Mersenne prime (A000668), or sigma(n)=3*2^(k-1), then n is in the sequence; are there any terms not of these forms? The last form includes the terms 15 and 1023; are there others like this? %C A066175 Is this sequence infinite? %C A066175 It is conjectured that there are infinitely many Mersenne primes. So this conjecture also supports that this sequence is infinite. Additionally, if n=2^k-1, where either k=1, or n is a Mersenne prime (A000668), or sigma(n)=3*2^(k-1), then A000217(n) divides sigma(A000217(n)). - _Altug Alkan_, Jul 25 2016 %e A066175 sigma(phi(sigma(31))) = sigma(phi(32)) = sigma(16) = 31. %t A066175 Select[Range[1, 10^6], DivisorSigma[1, EulerPhi[DivisorSigma[1, # ]]]==#&] %Y A066175 Cf. A000217, A000668. %K A066175 nonn,more %O A066175 1,2 %A A066175 _Joseph L. Pe_, Dec 15 2001 %E A066175 Edited by _Dean Hickerson_, Feb 20 2002 %E A066175 a(11) from _Jud McCranie_, Jun 23 2005; no more terms < 4000000000.