OFFSET
2,3
COMMENTS
Solutions such as 181^2+7 = 32^2 = 8^5 = 2^15 are counted only once. A094596 counts this as three solutions. Bugeaud, Mignotte and Siksek find all solutions for n <= 100.
LINKS
Yann Bugeaud, Maurice Mignotte and Samir Siksek, Classical and modular approaches to exponential Diophantine equations II. The Lebesgue-Nagell equation
EXAMPLE
a(4) = 2 because there are two solutions: 2^2+4=2^3 and 11^2+4=5^3.
MATHEMATICA
Table[cnt=0; xLst={}; Do[x=Sqrt[y^k-n]; If[IntegerQ[x] && !MemberQ[xLst, x], cnt++; AppendTo[xLst, x]], {k, 3, 20}, {y, 600}]; cnt, {n, 2, 100}]
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
T. D. Noe, May 13 2004
STATUS
approved