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 A159886 #33 Dec 16 2024 01:58:22 %S A159886 12,18,24,31,32,42,48,54,56,60,72,80,84,90,96,98,104,108,114,120,124, %T A159886 126,128,132,140,144,152,156,168,180,182,186,192,210,216,224,228,234, %U A159886 240,248,252,264,270,272,280,288,294,308,312,320,324,336,342,360,372,378,384,390 %N A159886 Values k such that sigma(x) = k has more than one solution, sigma = A000203. %C A159886 Numbers k with A054973(k) >= 2. Numbers k which occur in A000203 more than once. %C A159886 Numbers k = A007609(n) with A007609(n+1) - A007609(n) = 0. %C A159886 Does this sequence have finite density? - _Franklin T. Adams-Watters_, Jun 18 2009 %C A159886 See A300869 for the odd terms, much less frequent since they can only occur for x = k^2 or 2*k^2. - _M. F. Hasler_, Mar 16 2018 %H A159886 Amiram Eldar, <a href="/A159886/b159886.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1095 from Franklin T. Adams-Watters) %H A159886 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp). %e A159886 a(1) = 12 as the multiplicity of the value 12 is 2: 12 = sigma(6) = sigma(11). %o A159886 (PARI) %o A159886 na(n) = local(v, s); v=vector(n);for(k=1,n,s=sigma(k);if(s<=n,v[s]++));v %o A159886 la(n) = local(v, r); v=na(n);r=[];for(k=1,n,if(v[k]>1,r=concat(r,[k])));r \\ _Franklin T. Adams-Watters_, Jun 18 2009 %o A159886 (PARI) is(k) = invsigmaNum(k) > 1; \\ _Amiram Eldar_, Dec 16 2024, using _Max Alekseyev_'s invphi.gp %Y A159886 Cf. A000203, A054973, A007609, A007368. %Y A159886 Subsequence of A002191. %Y A159886 Odd terms are listed in A300869. %K A159886 nonn %O A159886 1,1 %A A159886 _Jaroslav Krizek_, Apr 25 2009 %E A159886 Edited and extended by _R. J. Mathar_, Apr 28 2009