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

1,2

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A066135.

Sequence in context: A334865 A103236 A141235 * A218969 A345291 A185973

Adjacent sequences: A199164 A199165 A199166 * A199168 A199169 A199170

Keyword

nonn

Author

Michel Lagneau, Nov 03 2011

Status

approved