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 A132631 #9 Jun 23 2024 13:28:46 %S A132631 2,4,6,10,12,16,18,20,22,24,28,30,36,40,42,46,52,58,60,66,70,72,78,82, %T A132631 88,94,96,100,102,106,108,112,120,126,130,136,138,148,150,156,162,166, %U A132631 172,178,180,190,192,196,198 %N A132631 Numbers k such that sigma(k+1)-k-1 divides sigma(k)-k, where sigma(k) is sum of positive divisors of n. %C A132631 Only even numbers. %H A132631 Harvey P. Dale, <a href="/A132631/b132631.txt">Table of n, a(n) for n = 1..1000</a> %e A132631 k=94 -> sigma(k)-k=1+2+47=50 sigma(k+1)-k-1=1+5+19=25 -> 50/25=2 %e A132631 k=120 -> sigma(k)-k=1+2+3+4+5+6+8+10+12+15+20+24+30+40+60=240 sigma(k+1)-k-1=1+11=12 -> 240/12=20 %p A132631 with(numtheory): P:=proc(k) if frac((sigma(k)-k)/(sigma(k+1)-k-1))=0 then k; fi; end: seq(P(n),n=2..200); %t A132631 Select[Range[2,200],Divisible[DivisorSigma[1,#]-#,DivisorSigma[1,#+1]-#-1]&] (* _Harvey P. Dale_, May 20 2017 *) %Y A132631 Cf. A132585, A132586, A132630. %K A132631 easy,nonn %O A132631 1,1 %A A132631 _Paolo P. Lava_ and _Giorgio Balzarotti_, Aug 27 2007