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 A132586 #18 Jul 28 2025 06:20:08 %S A132586 8,24,8925,32445,118540859325 %N A132586 Numbers k such that sigma(k+1)-k-2 divides sigma(k)-k-1, where sigma(k) is sum of positive divisors of k and the ratio is greater than zero. %C A132586 The banal case of ratio equal to zero is excluded. In fact if k is a prime than sigma(k)-k-1=0. Therefore the ratio with sigma(k+1)-k-2 is equal to zero. Is this sequence finite? %C A132586 a(6), if it exists, is larger than 10^13. - _Giovanni Resta_, Jul 13 2015 %C A132586 No more terms < 2.7*10^15. - _Jud McCranie_, Jul 27 2025 %e A132586 n=8 -> sigma(8)=1+2+4+8 -> sigma(n)-n-1=2+4=6. %e A132586 n+1=9 -> sigma(9)=1+3+9 -> sigma(n+1)-n-2=3. %e A132586 6/3 = 2 (integer >0) %p A132586 with(numtheory); P:=proc(n) local a,i; for i from 1 by 1 to n do if sigma(i+1)-i-2>0 then a:=(sigma(i)-i-1)/(sigma(i+1)-i-2); if a>0 and trunc(a)=a then print(i); fi; fi; od; end: P(100000); %Y A132586 Cf. A002961, A058072, A058073, A132585. %K A132586 hard,more,nonn %O A132586 1,1 %A A132586 _Paolo P. Lava_ and _Giorgio Balzarotti_, Aug 23 2007 %E A132586 a(5) from _Donovan Johnson_, Aug 31 2008