A199167 Smallest number k such that the sum of the n-th powers of the divisors of k is divisible by n.

1, 3, 2, 15, 8, 12, 4, 105, 2, 3, 43, 60, 9, 12, 8, 945, 67, 300, 37, 240, 5, 48, 137, 420, 8, 5, 2, 60, 173, 12, 16, 10395, 86, 13, 76, 2100, 73, 147, 8, 1680, 163, 4800, 257, 240, 8, 3072, 281, 3780, 4, 3, 101, 60, 211, 14700, 8, 420, 32, 17, 353, 8400, 169

Offset: 1

Author

Michel Lagneau, Nov 03 2011

Keywords

• nonn

Examples

			a(6) = 12 because the divisors of 12 are 1, 2, 3, 4, 6, 12 and 1^6 + 2^6 + 3^6 + 4^6 + 6^6 + 12^6 =  3037530 = 6*506255.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A066135.

Programs

Maple

with(numtheory):
a:= proc(n) local k;
      for k while irem (add (d &^n mod n, d=divisors(k)), n)<>0
      do od; k
    end:
seq (a(n), n=1..63);

Mathematica

snk[n_]:=Module[{k=1},While[!Divisible[DivisorSigma[n,k],n],k++];k]; Array[ snk,70] (* Harvey P. Dale, Jun 07 2016 *)

PARI

a(n)=my(k);while(sigma(k++,n)%n,);k \\ Charles R Greathouse IV, Nov 03 2011