A082120 Smallest difference > 1 between d and n/d for any divisor d of n.

2, 3, 4, 5, 6, 2, 8, 3, 10, 4, 12, 5, 2, 6, 16, 3, 18, 8, 4, 9, 22, 2, 24, 11, 6, 3, 28, 7, 30, 4, 8, 15, 2, 5, 36, 17, 10, 3, 40, 11, 42, 7, 4, 21, 46, 2, 48, 5, 14, 9, 52, 3, 6, 10, 16, 27, 58, 4, 60, 29, 2, 12, 8, 5, 66, 13, 20, 3, 70, 6, 72, 35, 10, 15, 4, 7, 78, 2, 24, 39, 82, 5

Offset: 3

Author

Ralf Stephan, Apr 04 2003

Keywords

• nonn
• easy

Comments

a(p) = p-1 for prime p.

Links

• Robert Israel, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A082119, A056737, A003681, A082121.

Programs

Maple

F:= proc(n) local p;
  p:= min(select(t -> t - n/t > 1, numtheory:-divisors(n)));
  p - n/p
end proc:
map(F, [$3..100]); # Robert Israel, Aug 12 2015

Mathematica

sd[n_]:=Min[Select[Abs[#-n/#]&/@Divisors[n],#>1&]]; Array[sd,90,3] (* Harvey P. Dale, Sep 28 2013 *)

PARI

for(n=3, 100, v=divisors(n); r=sqrt(n); t=0; for(k=1, length(v), if(v[k]>=r, t=k; break)); if(v[t]^2==n, u=t, u=t-1); if(v[t]-v[u]<2, u=u-1; t=t+1); print1(v[t]-v[u]", "))