A192294 - OEIS

%I #16 Sep 20 2013 11:34:35

%S 3,5,7,13,17,53,67,137,203,247,473,787,5197,6143,13513,15593,22523,

%T 30713,50243,67567,285863,337837,427927,795217,1148647,2139637,

%U 5743237,8393963,11869357,17229713,32094563,74662087,109121513,132094463,632904773,763850587

%N 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 Where record values of Sum(1/d*_n) occur.

%C 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 3  -> 1/2 = 0.5

%e 5  -> 1/3+1/2 = 5/6 = 0.8333…

%e 7  -> 1/2+1/3+1/5 = 1.0333…

%e 13 -> 1/2+1/3+1/5+1/9 = 1.1444…  etc.

%p with(numtheory);

%p P:=proc(j)

%p local b,h,m,r;

%p b:=0;

%p for m from 3 to j  do

%p   h:=0;

%p   for r from 2 to m-1 do if abs((m mod r)-r/2)<1 then h:=h+1/r; fi; od;

%p   if h>b then b:=h; print(m); fi;

%p od;

%p end:

%p P(100000);

%Y Cf. A004394, A066417, A192269.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Sep 02 2011

%E a(21)-a(36) from _Donovan Johnson_, Sep 07 2011