A338150 a(n) is the least j >= 2 such that (n+1)^A338136(n) mod n^j is a perfect power > 1.

4, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2

Offset

2,1

Links

Table of n, a(n) for n=2..88.

Formula

(n+1)^A338136(n) mod n^A338150(n) = A338151(n).

Example

a(2) = 4 because A338136(2) = 6 and 3^6 mod 2^4 = 3^2.
a(13) = 2 because A338136(13) = 2 and 14^2 mod 13^2 = 3^3.

Maple

g:= proc(n) local k, x, j, F;
  for k from 2 to n-2 do
   x:= (n+1)^k;
   for j from 2 to floor(k*log[n](n+1)) do
     F:= ifactors(x mod (n^j))[2];
     if igcd(op(map(t -> t[2], F))) > 1 then return j fi
  od od
end proc:
g(2):= 4: g(3):= 2:
map(g, [$2..40]);

Crossrefs

Cf. A001597, A338136, A338151.

Sequence in context: A136714 A280135 A297825 * A303577 A010314 A080133

Adjacent sequences: A338147 A338148 A338149 * A338151 A338152 A338153

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Oct 12 2020

Extensions

More terms from Jinyuan Wang, Oct 17 2020

Status

approved