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 A387406 #21 Aug 31 2025 12:57:13
%S A387406 6,18,28,54,117,162,196,486,496,775,1372,1458,1521,4374,8128,9604,
%T A387406 13122,15376,19773,24025,39366,67228,88723,118098,257049,354294,
%U A387406 470596,476656,744775,796797,1032256,1062882,2896363,3188646,3294172,3341637,6725201,9565938,12326221,14776336,23059204,23088025,25774633,27237961
%N A387406 Numbers k such that sigma(A253560(k)) / A253560(k) is equal to (sigma(k)+1) / k, where A253560(k) = k multiplied by its largest prime factor.
%C A387406 Terms k for which sigma(k/A053585(k)) = A006530(k). This further entails that A001221(k) = 2 [See A023194].
%H A387406 Antti Karttunen, <a href="/A387406/b387406.txt">Table of n, a(n) for n = 1..58</a> (larger b-file needed)
%H A387406 C. A. Holdener and J. A. Holdener, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Holdener/holdener4.html">Characterizing Quasi-Friendly Divisors</a>, Journal of Integer Sequences, Vol. 23 (2020), Article 20.8.4.
%H A387406 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A387406 fk[k_]:=k*FactorInteger[k][[-1,1]];Select[Range[10^6],DivisorSigma[1,fk[#]]/fk[#]==(DivisorSigma[1,#]+1)/#&] (* _James C. McMahon_, Aug 31 2025 *)
%o A387406 (PARI)
%o A387406 A253560(n) = if (n==1, 1, n*vecmax(factor(n)[, 1]));
%o A387406 isA387406(n) = { my(x=A253560(n)); ((sigma(x)/x) == ((sigma(n)+1)/n)); };
%Y A387406 Cf. A000203, A001221, A006530, A023194, A053585, A253560, A387405.
%Y A387406 Subsequences: A000396 (even terms only), A240991 (conjectured, if true, then A000396 has only even terms).
%K A387406 nonn,new
%O A387406 1,1
%A A387406 _Antti Karttunen_, Aug 30 2025