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 A146567 #22 Nov 16 2017 15:52:24 %S A146567 2,12,24,56,60,132,1260 %N A146567 Numbers n such that n*sigma_0(n)/(n+sigma_0(n)) = c, c an integer. %C A146567 A000027(n)*A000005(n)/(A000027(n)+A000005(n))=c, c an integer. %C A146567 No other term < 5000000. - _Emeric Deutsch_, Nov 09 2008 %C A146567 No other term < 10000000. - _Michel Marcus_, Jun 02 2013 %C A146567 For a given n let x be the minimal natural number such that n*x/(n+x)=c. I conjecture: from a certain n onward, x>sigma_0(n) for all n. Thus, there is no other solution bigger than 1260, and this sequence is finite. - _Ctibor O. Zizka_, Sep 13 2015 %C A146567 This sequence is complete. The finiteness proof is analogous to that of A152491, after observing that sigma_0(n)^2 < n for n > 1260 (see A034884). - _Giovanni Resta_, Sep 13 2015 %p A146567 with(numtheory): a:=proc (n) if type(n*tau(n)/(n+tau(n)), integer) = true then n else end if end proc: seq(a(n),n=1..200000); # _Emeric Deutsch_, Nov 09 2008 %Y A146567 Cf. A000027, A000005, A034884. %K A146567 nonn,fini,full %O A146567 1,1 %A A146567 _Ctibor O. Zizka_, Nov 01 2008 %E A146567 Corrected and extended (one term) by _Emeric Deutsch_, Nov 09 2008