

A299438


a(n) is the smallest number k such that there does not exist k numbers in the range [1..n] whose product is equal to its sum or 1 if no such number exists.


2



2, 3, 4, 6, 6, 15, 15, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 80, 80, 80, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114
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OFFSET

1,1


COMMENTS

If a(n) > 0 for all n, then sequence is nondecreasing and a(n) > n.
For n >= 38, a(n) appears to follow the pattern: a(n) = k_m for k_{m1} <= n < k_m, for a sequence of numbers {k_m} = {38, 114, 174, 444, 4354, ... }.
Conjecture: a(n) > 0 for all n.


LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..450


EXAMPLE

a(1) > 1 since the product of the list (1) is the same as its product. a(1) = 2 since the product of the list (1,1) = 1 which is not the same as its sum (= 2).
a(2) > 2 since (2,2) has both product and sum equal to 2. Similarly a(3) > 3 since (1,2,3) has both sum and product equal to 6.


CROSSREFS

Cf. A299439.
Sequence in context: A002729 A135510 A265398 * A030209 A265399 A138588
Adjacent sequences: A299435 A299436 A299437 * A299439 A299440 A299441


KEYWORD

nonn


AUTHOR

Chai Wah Wu, Feb 19 2018


STATUS

approved



