A125314 Smallest number k>1 such that Sum_{i=1..k} i^n divides Product_{i=1..k} i^n.

3, 7, 3, 31, 13, 1556, 733, 89037, 1441, 668073

Offset: 1

Author

Alexander Adamchuk, Jan 18 2007

Keywords

• hard
• more
• nonn

Comments

Sum[ i^n, {i,1,k} ] = Zeta[ -n ] - Zeta[ -n, k+1 ]. Product[ i^n, {i,1,k} ] = (k!)^n.

a(11) > 1091730. - Robert G. Wilson v, Jan 25 2007

Programs

Mathematica

f[n_] := Block[{k = 2, p = s = 1}, While[p = p*k; s = s + k^n; PowerMod[p, n, s] != 0, k++ ]; k]; (* Robert G. Wilson v *)

Extensions

a(8)-a(10) from Robert G. Wilson v, Jan 25 2007