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 A378267 #5 Nov 21 2024 05:40:27
%S A378267 1,6,24,120,672,4320,26208,30240,524160,2178540,8714160,8910720,
%T A378267 17428320,45532800,132723360,208565280,240589440,470564640,668304000,
%U A378267 1307124000,5228496000,10805558400,14182439040,31998395520,159991977600
%N A378267 Numbers k that have a record number of common divisors with sigma(k).
%C A378267 Indices of records in A073802.
%C A378267 This sequence is infinite since A073802 is unbounded. For example, for any odd number m we have A073802(2^(m-1)*(2^m-1)) >= A000005(m) and the number of divisors of odd numbers is unbounded.
%C A378267 The corresponding record values are 1, 4, 6, 16, 24, 40, 60, 96, 144, 216, 240, 336, ... .
%C A378267 a(26) <= 799959888000.
%t A378267 seq[kmax_] := Module[{d, dmax = 0, s = {}}, Do[d = DivisorSigma[0, GCD[k, DivisorSigma[1, k]]]; If[d > dmax, dmax = d; AppendTo[s, k]], {k, 1, kmax}]; s]; seq[10^6]
%o A378267 (PARI) lista(kmax) = {my(d, dmax = 0); for(k = 1, kmax, d = numdiv(gcd(k, sigma(k))); if(d > dmax, dmax = d; print1(k, ", ")));}
%Y A378267 Cf. A000005, A000203 (sigma), A014567, A073802, A216793.
%K A378267 nonn,more
%O A378267 1,2
%A A378267 _Amiram Eldar_, Nov 21 2024