A243981 - OEIS

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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

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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