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.

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

1,1

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.

Links

Table of n, a(n) for n=1..36.

Example

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.

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);

Crossrefs

Cf. A004394, A066417, A192269.

Sequence in context: A173641 A153645 A106878 * A227531 A079481 A291867

Adjacent sequences: A192291 A192292 A192293 * A192295 A192296 A192297

Keyword

nonn

Author

Paolo P. Lava, Sep 02 2011

Extensions

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

Status

approved