Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #22 Nov 16 2017 15:52:24
%S 2,12,24,56,60,132,1260
%N Numbers n such that n*sigma_0(n)/(n+sigma_0(n)) = c, c an integer.
%C A000027(n)*A000005(n)/(A000027(n)+A000005(n))=c, c an integer.
%C No other term < 5000000. - _Emeric Deutsch_, Nov 09 2008
%C No other term < 10000000. - _Michel Marcus_, Jun 02 2013
%C 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 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 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 Cf. A000027, A000005, A034884.
%K nonn,fini,full
%O 1,1
%A _Ctibor O. Zizka_, Nov 01 2008
%E Corrected and extended (one term) by _Emeric Deutsch_, Nov 09 2008