OFFSET
1,1
COMMENTS
At most one of a(n) - 1 and 2*a(n)-1 are composite. More precisely, a(n) are those positive integers such that exactly one of product(s)*(a(n)+sum(s)-k-2)+1 can be factored as (product(s)*p-1)*(product(s)*q-1), where s varies over all multisets of k positive integers and 1 < p <= q < a(n). The first statement is given by considering s = {} and s = {2}. a(50) is greater than 10^4.
LINKS
Michael W. Ecker, When Does a Sum of Positive Integers Equal Their Product?, Mathematics Magazine 75(1), 2002, pp. 41-47.
EXAMPLE
a(5) = 12 because {2,2,2,2,1,1,1,1,1,1,1,1} and {12,2,1,1,1,1,1,1,1,1,1,1} are the only multisets of size 12 where the sum equals the product.
CROSSREFS
KEYWORD
nonn
AUTHOR
Nathaniel Gregg, Apr 11 2021
STATUS
approved