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 A383482 #27 May 04 2025 23:44:16 %S A383482 1,6,9,28,216,360,496,2016,2401,8128,16758,182520,884736,1022112, %T A383482 1352328,1571328,1935360,2678400,33550336,54758400,101382400, %U A383482 119533176,136808280,163298502,198288000,618591192,691022088,782481673,796663296,1137067008,1275418369,1303102080 %N A383482 Integers k such that sigma(k)/k - 1 is a rational square. %H A383482 Michel Marcus, <a href="/A383482/b383482.txt">Table of n, a(n) for n = 1..40</a> %e A383482 6 is a term because sigma(6)/6 - 1 = 2 - 1 = 1, a square; like for all perfect numbers. %e A383482 9 is a term because sigma(9)/9 - 1 = 13/9 - 1 = 4/9, a square. %t A383482 q[k_] := And @@ IntegerQ /@ Sqrt[NumeratorDenominator[DivisorSigma[-1, k] - 1]]; Select[Range[2*10^6], q] (* _Amiram Eldar_, Apr 28 2025 *) %o A383482 (PARI) isok(k) = issquare(sigma(k)/k - 1); %Y A383482 Cf. A000203 (sigma), A069070. %Y A383482 Subsequences: A000396 (perfect numbers), A046060 (5-multiperfect numbers), A381321. %Y A383482 Cf. A218404 (for those terms with sigma(x)/x = 13/4). %K A383482 nonn %O A383482 1,2 %A A383482 _Michel Marcus_, Apr 28 2025 %E A383482 a(30)-a(32) from _Jinyuan Wang_, Apr 28 2025