cp's OEIS Frontend

A340806 a(n) = Sum_{k=1..n-1} (k^n mod n).

%I A340806 #12 Feb 14 2021 04:03:48
%S A340806 0,1,3,2,10,13,21,4,27,45,55,38,78,77,105,8,136,93,171,146,210,209,
%T A340806 253,172,250,325,243,294,406,365,465,16,528,561,595,402,666,665,741,
%U A340806 372,820,673,903,726,945,897,1081,536,1029,1125,1275,1170,1378,765,1485
%N A340806 a(n) = Sum_{k=1..n-1} (k^n mod n).
%H A340806 Sebastian Karlsson, <a href="/A340806/b340806.txt">Table of n, a(n) for n = 1..10000</a>
%F A340806 a(n) = n*A010848(n)/2, if n is odd.
%F A340806 a(n) = n*(n-1)/2, if n is both odd and squarefree.
%F A340806 a(p^e) = (1/2)*(p-1)*p^(2*e-1), if p is an odd prime.
%F A340806 a(2^e) = 2^(e-1).
%p A340806 a:= n-> add(k&^n mod n, k=1..n-1):
%p A340806 seq(a(n), n=1..55);  # _Alois P. Heinz_, Feb 13 2021
%o A340806 (Python)
%o A340806 def a(n):
%o A340806     return sum([pow(k,n,n) for k in range(1, n)])
%o A340806 for n in range(1, 56):
%o A340806     print(a(n), end=', ')
%o A340806 (PARI) a(n) = sum(k=1, n-1, lift(Mod(k, n)^n)); \\ _Michel Marcus_, Jan 22 2021
%Y A340806 Cf. A010848, A048153, A048155, A094264, A121706, A195637, A195812, A202034.
%K A340806 nonn
%O A340806 1,3
%A A340806 _Sebastian Karlsson_, Jan 22 2021