cp's OEIS Frontend

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

%I A199167 #20 Jun 07 2016 19:11:16
%S A199167 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 A199167 8,5,2,60,173,12,16,10395,86,13,76,2100,73,147,8,1680,163,4800,257,
%U A199167 240,8,3072,281,3780,4,3,101,60,211,14700,8,420,32,17,353,8400,169
%N A199167 Smallest number k such that the sum of the n-th powers of the divisors of k is divisible by n.
%H A199167 Charles R Greathouse IV, <a href="/A199167/b199167.txt">Table of n, a(n) for n = 1..200</a>
%e A199167 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 A199167 with(numtheory):
%p A199167 a:= proc(n) local k;
%p A199167       for k while irem (add (d &^n mod n, d=divisors(k)), n)<>0
%p A199167       do od; k
%p A199167     end:
%p A199167 seq (a(n), n=1..63);
%t A199167 snk[n_]:=Module[{k=1},While[!Divisible[DivisorSigma[n,k],n],k++];k]; Array[ snk,70] (* _Harvey P. Dale_, Jun 07 2016 *)
%o A199167 (PARI) a(n)=my(k);while(sigma(k++,n)%n,);k \\ _Charles R Greathouse IV_, Nov 03 2011
%Y A199167 Cf. A066135.
%K A199167 nonn
%O A199167 1,2
%A A199167 _Michel Lagneau_, Nov 03 2011