OFFSET
1,4
COMMENTS
The smallest set is obtained by taking the largest such multiset (A341865(n)) and replacing the largest proper subset that is also a product-sum multiset with its product. A singleton would always be the smallest product-sum multiset, so those are excluded except for prime n where no nontrivial multisets exist.
FORMULA
EXAMPLE
For n = 12, the set of size a(n) = 6 is {1,1,1,1,2,6}.
PROG
(PARI) a(n) = if (n==1, 1, my(p=vecmin(factor(n)[, 1])); (n/p-1)*(p-1) + 1); \\ Michel Marcus, Feb 26 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Nathaniel Gregg, Feb 22 2021
STATUS
approved