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 A159939 #16 Nov 21 2024 13:28:07 %S A159939 1,9,225,729,18225,65025,140625,531441,5267025,11390625,13286025, %T A159939 18792225,40640625,87890625,1522170225,2197265625,3291890625, %U A159939 3839661225,5430953025,7119140625,8303765625,11745140625,25400390625 %N A159939 Odd solutions of phi(sigma(k)) = sigma(phi(k)). %C A159939 sigma is the multiplicative sum-of-divisors function. %C A159939 phi is Euler's totient. %C A159939 Complete through 25558816403. %C A159939 All given here are products of powers of consecutive Fermat primes based on generalized repunit primes; see links. %C A159939 It is conjectured (see links) that all odd solutions are of this form, for which at least 10130 solutions are known. %C A159939 a(24) > 10^11, if it exists. - _Amiram Eldar_, Nov 21 2024 %D A159939 Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B42, pp. 150-152. %D A159939 Oystein Ore, Number Theory and Its History, 1948, reprinted 1988, Dover, ISBN-10: 0486656209, pp. 88 et seq., 109 et seq. %H A159939 Walter Nissen, <a href="http://upforthecount.com/math/sigmaphi.html">phi(sigma(n)) = sigma(phi(n))</a>. %e A159939 sigma(9) = 13, phi(9) = 6, sigma(6) = phi(13) = 12, so 9 is in the sequence. %o A159939 (PARI) isok(n) = (n % 2) && (eulerphi(sigma(n)) == sigma(eulerphi(n))) \\ _Michel Marcus_, Jul 23 2013 %Y A159939 Cf. A000203, A000010, A033632, A019434. %K A159939 nonn %O A159939 1,2 %A A159939 _Walter Nissen_, Apr 26 2009 %E A159939 Edited by _Charles R Greathouse IV_, Oct 28 2009 %E A159939 a(1) = 1 inserted by _Amiram Eldar_, Nov 21 2024