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

2,2

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

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

Prog

(PARI) for(n=2, 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]<1, u=u-1; t=t+1); print1(v[t]-v[u]", "))

Crossrefs

Cf. A082120, A056737.

Sequence in context: A069817 A071439 A100941 * A129708 A071518 A330342

Adjacent sequences: A082116 A082117 A082118 * A082120 A082121 A082122

Keyword

nonn,easy

Author

Ralf Stephan, Apr 04 2003

Status

approved