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%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
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