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 A381321 #61 May 22 2025 12:38:59 %S A381321 1,6,28,216,360,496,2016,8128,16758,1571328,1935360,2678400,33550336, %T A381321 54758400,101382400,1685013120 %N A381321 Numbers k such that sigma(k)/k - 1 equals (sigma(m)/m - 1)^2 for some m <= k. %C A381321 For any perfect number sigma(k)/k - 1 = 1, so all perfect numbers are terms. %C A381321 2016 = 2^(6-1)*(2^6-1) is of the form 2^(k-1)*(2^k - 1) like the perfect numbers. %C A381321 4428914688 from A383482 and 155086041146982400 from A218404 are terms. - _Michel Marcus_, May 22 2025 %H A381321 David C. Luo, <a href="https://arxiv.org/abs/1803.10816">Generalizing the Abundancy of an Integer</a>, arXiv:1803.10816 [math.NT], 2018-2019. %e A381321 216 is a term since sigma(216)/216 - 1 = (4/3)^2 and sigma(12)/12 - 1 = 4/3. %o A381321 (PARI) isok(k)=my(t=(sigma(k)-k)*k); if(issquare(t), my(r=sqrtint(t)/k+1, s=denominator(r)); forstep(m=s, k, s, if(sigma(m)/m==r, return(1)) )); 0 \\ _Andrew Howroyd_, Mar 03 2025 %Y A381321 Cf. A000396, A006516, A243473/A017666. %Y A381321 Subsequence of A383482. %K A381321 nonn,more %O A381321 1,2 %A A381321 _Leo Hennig_, Feb 21 2025 %E A381321 a(15)-a(16) from _Michel Marcus_, Mar 05 2025