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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A209747 A117744 A091732 * A109746 A286365 A061020

Adjacent sequences:  A299436 A299437 A299438 * A299440 A299441 A299442

KEYWORD

nonn

AUTHOR

Chai Wah Wu, Feb 19 2018

STATUS

approved

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Last modified June 16 12:38 EDT 2019. Contains 324152 sequences. (Running on oeis4.)