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.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A057897, A057899.

Sequence in context: A194086 A342723 A164659 * A094293 A338156 A335122

Adjacent sequences: A057895 A057896 A057897 * A057899 A057900 A057901

Keyword

nonn

Author

Henry Bottomley, Sep 26 2000

Status

approved