OFFSET
2,3
COMMENTS
Corresponding solutions for x are 256 (2^(2^3)) at n = 2, 19683 (3^(3^2)) at n = 3 and n^(n^2) for all n > 3.
Further solution pairs are of the form y = n^(n^k) - n^(2+k) and x = n^(n^(1+k)) with k > 0.
FORMULA
E.g.f.: 1/(1 + LambertW(-x)) - x*(1 + 3*x + x^2)*exp(x) + 2*x^2, where LambertW() is the Lambert W-function.
a(n) = n^n - n^3 for n > 2.
PROG
(PARI) a(n) = max(0, n^n-n^3)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thomas Scheuerle, May 01 2023
STATUS
approved