

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
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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^kk) = 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



