A094755 Least integer value of (1 + 2^n + 3^n + ... + k^n)/(1 + 2 + 3 + ... + k), k > 1.

1, 3, 3, 167, 11, 489, 43, 282407, 171, 110865, 683, 3710553451913, 2731, 27323481, 10923, 1293248801687, 43691, 6910715937, 174763, 2983746256027727, 699051, 1762357129833, 2796203, 734630194457006903941170593, 11184811, 450614156030769, 44739243

Offset: 1

Author

Amarnath Murthy, May 29 2004

Keywords

• nonn

Examples

			a(4) = (1^4 + 2^4 + 3^4 + 4^4 + 5^4 + 6^4 + 7^4)/(1+2+3+4+5+6+7) = 4676/28 = 167, k = 7.
a(5) = (1^5 + 2^5)/(1 + 2) = 11, k = 2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..719

Crossrefs

Cf. A000217, A094756.

Programs

Maple

a:= proc(n) option remember; local k,r,s,t; s, t:=1$2;
      for k from 2 do s, t:= s+k, t+k^n;
        if irem(t, s, 'r')=0 then return r fi
      od:
    end:
seq(a(n), n=1..28);  # Alois P. Heinz, Mar 07 2024

Mathematica

f[n_] := Block[{k = 2}, While[s = 2Sum[i^n, {i, k}]/(k(k + 1)); !IntegerQ[s], k++ ]; s]; Table[ f[n], {n, 25}] (* Robert G. Wilson v, Jun 02 2004 *)

Extensions

Edited and extended by Robert G. Wilson v, Jun 02 2004