A192294 Numbers n such that Sum(1/d*_n)>Sum(1/d*_m) for all m

3, 5, 7, 13, 17, 53, 67, 137, 203, 247, 473, 787, 5197, 6143, 13513, 15593, 22523, 30713, 50243, 67567, 285863, 337837, 427927, 795217, 1148647, 2139637, 5743237, 8393963, 11869357, 17229713, 32094563, 74662087, 109121513, 132094463, 632904773, 763850587

Offset: 1

Author

Paolo P. Lava, Sep 02 2011

Keywords

• nonn

Comments

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

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.

Examples

			3  -> 1/2 = 0.5
5  -> 1/3+1/2 = 5/6 = 0.8333…
7  -> 1/2+1/3+1/5 = 1.0333…
13 -> 1/2+1/3+1/5+1/9 = 1.1444…  etc.
		

Crossrefs

Cf. A004394, A066417, A192269.

Programs

Maple

with(numtheory);
P:=proc(j)
local b,h,m,r;
b:=0;
for m from 3 to j  do
  h:=0;
  for r from 2 to m-1 do if abs((m mod r)-r/2)<1 then h:=h+1/r; fi; od;
  if h>b then b:=h; print(m); fi;
od;
end:
P(100000);

Extensions

a(21)-a(36) from Donovan Johnson, Sep 07 2011