A082119 Smallest positive difference between d and n/d for any divisor d of n.

1, 2, 3, 4, 1, 6, 2, 8, 3, 10, 1, 12, 5, 2, 6, 16, 3, 18, 1, 4, 9, 22, 2, 24, 11, 6, 3, 28, 1, 30, 4, 8, 15, 2, 5, 36, 17, 10, 3, 40, 1, 42, 7, 4, 21, 46, 2, 48, 5, 14, 9, 52, 3, 6, 1, 16, 27, 58, 4, 60, 29, 2, 12, 8, 5, 66, 13, 20, 3, 70, 1, 72, 35, 10, 15, 4, 7, 78, 2, 24, 39, 82, 5

Offset: 2

Author

Ralf Stephan, Apr 04 2003

Keywords

• nonn
• easy

Comments

a(n) = A056737(n) for nonsquare n. a(p) = p-1 for prime p.

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A082120, A000037 (nonsquares), A056737.

Programs

Maple

with(numtheory):
a:= n-> min(seq((h-> `if`(h>0, h, NULL))(d-n/d), d=divisors(n))):
seq(a(n), n=2..100);  # Alois P. Heinz, Nov 12 2014

Mathematica

a[n_] := Min[Table[If[# > 0, #, Nothing]&[d-n/d], {d, Divisors[n]}]];
Table[a[n], {n, 2, 100}] (* Jean-François Alcover, Jan 13 2025, after Alois P. Heinz *)

PARI

a(n) = my(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]<1, u=u-1; t=t+1); v[t]-v[u];