

A243981


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


1



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

Cf. A056737, A060794, A076388, A082119.
Sequence in context: A079124 A242071 A176910 * A056737 A289144 A008797
Adjacent sequences: A243978 A243979 A243980 * A243982 A243983 A243984


KEYWORD

nonn,look


AUTHOR

Paul Richards, Nov 11 2014


STATUS

approved



