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A057898
Largest number such that n = m^a(n) - a(n) with m a positive integer; i.e., where (n + a(n))^(1/a(n)) is a positive integer.
3
1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 5, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,2
COMMENTS
It may be that positive integers can be written as n = m^k - k (with m and k > 1) in at most one way [checked up to 10000] as well as with k = 1 and m = n+1.
LINKS
EXAMPLE
a(5) = 3 since 5 = 2^3 - 3.
MAPLE
N:= 200: # for a(1)..a(N)
V:= Vector(N, 1):
for k from 2 while 2^k-k <= N do
for m from 2 do
v:= m^k-k;
if v > N then break fi;
V[v]:= k;
od;
od:
convert(V, list); # Robert Israel, Sep 04 2020
CROSSREFS
Sequence in context: A194086 A342723 A164659 * A094293 A338156 A335122
KEYWORD
nonn
AUTHOR
Henry Bottomley, Sep 26 2000
STATUS
approved