A299439 a(n) is the smallest number k such that there exists n numbers in the range [1..k] whose product is equal to its sum.

1, 2, 3, 4, 2, 6, 4, 3, 5, 4, 4, 2, 3, 5, 8, 6, 5, 4, 3, 7, 3, 8, 5, 24, 4, 4, 2, 6, 4, 3, 7, 5, 5, 12, 12, 8, 5, 8, 6, 4, 4, 3, 8, 15, 6, 7, 3, 10, 9, 6, 5, 5, 7, 8, 4, 4, 4, 2, 7, 9, 6, 6, 6, 4, 3, 14, 10, 8, 9, 5, 5, 5, 3, 7, 11, 16, 9, 12, 6, 27, 5, 10, 8, 8

Offset

1,2

Comments

For all n > 1, 1 < a(n) <= n since the list (1,..,1,2,n) has both sum and product equal to 2n.

Numbers n such that a(n) = n: 1, 2, 3, 4, 6, 24, 114, 174, 444, ...

Conjecture: the next number for which a(n) = n is 4354 (see A299438).

Links

Chai Wah Wu, Table of n, a(n) for n = 1..2000

Formula

a(2^k-k) = 2 for k > 1.

Example

Examples of n numbers in the range [1..a(n)] whose product is equal to its sum:
n = 1:  (1)
n = 2:  (2, 2)
n = 3:  (1, 2, 3)
n = 4:  (1, 1, 2, 4)
n = 5:  (1, 1, 2, 2, 2)
n = 6:  (1, 1, 1, 1, 2, 6)
n = 7:  (1, 1, 1, 1, 1, 3, 4)
n = 8:  (1, 1, 1, 1, 1, 2, 2, 3)
n = 9:  (1, 1, 1, 1, 1, 1, 1, 3, 5)
n = 10: (1, 1, 1, 1, 1, 1, 1, 1, 4, 4)

Crossrefs

Cf. A299438.

Sequence in context: A366481 A361697 A091732 * A109746 A286365 A345061

Adjacent sequences: A299436 A299437 A299438 * A299440 A299441 A299442

Keyword

nonn

Author

Chai Wah Wu, Feb 19 2018

Status

approved