A199167 - OEIS

%I #20 Jun 07 2016 19:11:16

%S 1,3,2,15,8,12,4,105,2,3,43,60,9,12,8,945,67,300,37,240,5,48,137,420,

%T 8,5,2,60,173,12,16,10395,86,13,76,2100,73,147,8,1680,163,4800,257,

%U 240,8,3072,281,3780,4,3,101,60,211,14700,8,420,32,17,353,8400,169

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

%H Charles R Greathouse IV, <a href="/A199167/b199167.txt">Table of n, a(n) for n = 1..200</a>

%e 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.

%p with(numtheory):

%p a:= proc(n) local k;

%p       for k while irem (add (d &^n mod n, d=divisors(k)), n)<>0

%p       do od; k

%p     end:

%p seq (a(n), n=1..63);

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

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

%Y Cf. A066135.

%K nonn

%O 1,2

%A _Michel Lagneau_, Nov 03 2011