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 A349760 #17 Dec 06 2021 03:12:34 %S A349760 84,90,108,126,132,140,150,156,180,198,220,224,228,234,252,260,276, %T A349760 294,300,306,308,315,336,342,348,350,352,360,364,372,380,396,414,416, %U A349760 420,432,444,460,476,486,490,492,495,500,504,516,522,525,528,532,540,550,558 %N A349760 Numbers k such that d(k) = A000005(k), sigma(k) = A000203(k) and phi(k) = A000010(k) are all abundant numbers (A005101). %C A349760 Sándor (2005) proved that this sequence is infinite by showing that it includes all the numbers of the form 11 * p^11 * k where p != 11 is a prime and k is any number coprime to 11*p. %H A349760 Amiram Eldar, <a href="/A349760/b349760.txt">Table of n, a(n) for n = 1..10000</a> %H A349760 József Sándor, <a href="https://blngcc.files.wordpress.com/2008/11/jozsel-sandor-selected-chaters-of-geometry-analysis-and-number-theory.pdf">Selected Chapters of Geometry, Analysis and Number Theory</a>, 2005, pp. 132-134. %e A349760 84 is a term since d(84) = 12, sigma(84) = 224 and phi(84) = 24 are all abundant numbers: sigma(12) = 28 > 2*12 = 24, sigma(224) = 504 > 2*224 = 448 and sigma(24) = 60 > 2*24 = 48. %t A349760 abQ[n_] := DivisorSigma[1, n] > 2*n; q[n_] := And @@ abQ /@ Join[DivisorSigma[{0, 1}, n], {EulerPhi[n]}]; Select[Range[500], q] %o A349760 (PARI) isab(k) = sigma(k) > 2*k; \\ A005101 %o A349760 isok(k) = my(f=factor(k)); isab(numdiv(f)) && isab(sigma(f)) && isab(eulerphi(f)); \\ _Michel Marcus_, Dec 03 2021 %Y A349760 Cf. A000005, A000010, A000203, A005101. %Y A349760 Subsequence of A349758. %K A349760 nonn %O A349760 1,1 %A A349760 _Amiram Eldar_, Nov 29 2021