OFFSET
1,1
COMMENTS
To minimize the sum of the parts whose product is k, all k, a(n) <= k < a(n+1) should be split into n parts.
FORMULA
a(n) = ceiling(((n+1)/n)^((n+1)*n)).
EXAMPLE
a(2) = 12 because 2*sqrt(11) is less than 3*11^(1/3), but 2*sqrt(12) is more than 3*12^(1/3).
a(3) = 32 because 3*31^(1/3) is less than 4*31^(1/4), but the inequality reverses at 32.
PROG
(PARI) a(n) = ceil(((n+1)/n)^((n+1)*n)) \\ Michel Marcus, Jul 26 2013
(PARI) a(n) = {k=1; while (n*k^(1/n) < (n+1)*k^(1/(n+1)), k++); return (k); } \\ Michel Marcus, Jul 26 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Joshua Zucker and Julian Zucker, Jun 27 2006
STATUS
approved