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A192294 Numbers n such that Sum(1/d*_n)>Sum(1/d*_m) for all m where d*_n and d*_m are the anti-divisors of n and m.

%I A192294 #16 Sep 20 2013 11:34:35
%S A192294 3,5,7,13,17,53,67,137,203,247,473,787,5197,6143,13513,15593,22523,
%T A192294 30713,50243,67567,285863,337837,427927,795217,1148647,2139637,
%U A192294 5743237,8393963,11869357,17229713,32094563,74662087,109121513,132094463,632904773,763850587
%N A192294 Numbers n such that Sum(1/d*_n)>Sum(1/d*_m) for all m<n, where d*_n and d*_m are the anti-divisors of n and m.
%C A192294 Where record values of Sum(1/d*_n) occur.
%C A192294 While sigma(n)/n>sigma(m)/m, where n>m, is equivalent to 1/sigma(n)>1/sigma(m) or even to Sum_(1/d_n)>Sum_(1/d_m), where d_n and d_m are the divisors of n and m, with the anti-divisors these equivalences do not hold.
%e A192294 3  -> 1/2 = 0.5
%e A192294 5  -> 1/3+1/2 = 5/6 = 0.8333…
%e A192294 7  -> 1/2+1/3+1/5 = 1.0333…
%e A192294 13 -> 1/2+1/3+1/5+1/9 = 1.1444…  etc.
%p A192294 with(numtheory);
%p A192294 P:=proc(j)
%p A192294 local b,h,m,r;
%p A192294 b:=0;
%p A192294 for m from 3 to j  do
%p A192294   h:=0;
%p A192294   for r from 2 to m-1 do if abs((m mod r)-r/2)<1 then h:=h+1/r; fi; od;
%p A192294   if h>b then b:=h; print(m); fi;
%p A192294 od;
%p A192294 end:
%p A192294 P(100000);
%Y A192294 Cf. A004394, A066417, A192269.
%K A192294 nonn
%O A192294 1,1
%A A192294 _Paolo P. Lava_, Sep 02 2011
%E A192294 a(21)-a(36) from _Donovan Johnson_, Sep 07 2011