A216439 Smallest k such that k*n^3 + 1 is an n-th power.

1, 1, 37, 791, 95051, 111748, 2277696793, 484679258335, 229930796172439, 79792266297612, 66954547910007962117, 337165646545, 45082285083777592171142467, 2379140952844779936142872, 60722942736706550906445847537201, 78033832840595333890814363993704319

Offset: 1

Author

Michel Lagneau, Sep 10 2012

Keywords

• nonn

Examples

			a(3) = 37 because 37*3^3 + 1 = 1000 = 10^3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..216

Crossrefs

Cf. A076943, A193746.

Programs

Maple

f:= proc(n) local S,x;
  S:= subs(1=n^3+1, map(t -> rhs(op(t)), [msolve(x^n-1, n^3)]));
  x:= min(S);
  (x^n-1)/n^3
end proc:
f(1):= 1:
map(f, [$1..20]); # Robert Israel, Aug 26 2020

Mathematica

a={}; Do[k = 2; While[ !IntegerQ[(k^n - 1)/n^3], k++ ]; AppendTo[a, (k^n-1)/n^3], {n, 1, 20}]; a