A082119 -id:A082119 - cp's OEIS frontend

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

Ralf Stephan, Apr 04 2003

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

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

Cf. A082119, A056737, A003681, A082121.

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

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

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]", "))

A243981 Minimum range of sets of natural numbers with a product of n.

Original entry on oeis.org

1, 2, 0, 4, 1, 6, 0, 0, 3, 10, 1, 12, 5, 2, 0, 16, 1, 18, 1, 4, 9, 22, 1, 0, 11, 0, 3, 28, 1, 30, 0, 8, 15, 2, 0, 36, 17, 10, 3, 40, 1, 42, 7, 2, 21, 46, 1, 0, 3, 14, 9, 52, 1, 6, 1, 16, 27, 58, 2, 60, 29, 2, 0, 8, 5, 66, 13, 20, 3, 70, 1, 72, 35, 2, 15, 4, 7, 78, 1, 0, 39, 82, 4, 12, 41, 26, 3, 88, 1, 6, 19, 28, 45, 14, 1, 96, 5, 2, 0

Offset: 2

Paul Richards, Nov 11 2014

The minimum difference between the largest and smallest values in the sets of positive integers with a product of n, excluding the singleton set {n}.

			For 45 the sets are {1,45}, {3,15}, {5,9}, {3,3,5} with differences of 44, 12, 4 and 2 respectively.  2 is the minimum and so a(45) = 2.

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

Cf. A056737, A060794, A076388, A082119.

a(n) <= A046665(n) for all composite n, a(p) = p - 1 for primes p. - Charlie Neder, Jan 13 2019

cp's OEIS Frontend

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

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