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
KEYWORD
nonn
AUTHOR
Chai Wah Wu, Feb 19 2018
STATUS
approved