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 A230538 #25 Mar 19 2017 01:17:58 %S A230538 1,976250,6276690,6542085247225 %N A230538 Numbers whose abundancy sigma(n)/n is a rational fourth power. %C A230538 Subsequence of A069070. %C A230538 Note that there exist several other large numbers with the same abundancy as a(3), that is sigma(6276690)/6276690 = 19837440/6276690 = 256/81. For this, consider the two numbers 559625737239 (3^10*23*107*3851) and 1373356918809 (3^6*23*137*547*1093), both of which have sigma(n)/n = 128/81. As they are coprime to the perfect numbers, except 6, it suffices to multiply them by those terms of A000396 to get an abundancy of 2*128/81 = 256/81. The smallest of these is the 14-digit number 15669520642692. - _Michel Marcus_, Oct 29 2013 %C A230538 It is also possible to get higher powers for sigma(n)/n, for instance, 1024/243 = (4/3)^5 with n=1556619120, 4096/729 = (4/3)^6 with n=1526227435825092000, 279936/78125 = (6/5)^7 with n=553131046875000, 1679616/390625 = (6/5)^8 with n=15487669312500000. - _Michel Marcus_, Oct 30 2013 %C A230538 6542085247225 is a term. - _Hiroaki Yamanouchi_, Sep 22 2014 %C A230538 a(5) > 10^13. - _Giovanni Resta_, Jun 16 2015 %e A230538 For n = 976250, sigma(n)/n = 2024352/976250 = 1296/625 = (6/5)^4. %o A230538 (PARI) isok(n) = ispower(sigma(n)/n, 4); \\ _Michel Marcus_, Oct 23 2013 %Y A230538 Cf. A069070 (square), A230043 (cube). %K A230538 nonn,bref,more %O A230538 1,2 %A A230538 _Michel Marcus_, Oct 23 2013 %E A230538 a(4) from _Giovanni Resta_, Jun 14 2015