OFFSET
1,1
COMMENTS
Row n of table A332065 lists all s for which there is some S subset of {1,...,m-1} with s^n = Sum_{x in S} x^n. This is the case for all sufficiently large s (cf. reference there). Here we give the largest integer not in this list.
EXAMPLE
For n=1, we have m^n = (m-1)^n + 1^n, so S = {1, m-1} is a solution for all m > 2, but 2^n > 1^n and therefore no solution with m = 2 = a(1).
For n=2, we have a solution to m^n = Sum_{x in S} x^n for S subset of {1,...,m-1} for all m > 8 (cf. FORMULA in A332065), but no solution with m = 8 = a(2).
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
M. F. Hasler, Apr 19 2020
EXTENSIONS
a(8) - a(12) from M. F. Hasler, Jul 23 2020
STATUS
approved