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

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

2,2

Comments

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}.

Links

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

Formula

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

Example

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.

Crossrefs

Cf. A056737, A060794, A076388, A082119.

Sequence in context: A079124 A242071 A176910 * A369657 A338824 A056737

Adjacent sequences: A243978 A243979 A243980 * A243982 A243983 A243984

Keyword

nonn,look

Author

Paul Richards, Nov 11 2014

Status

approved