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

0, 1, 3, 2, 10, 13, 21, 4, 27, 45, 55, 38, 78, 77, 105, 8, 136, 93, 171, 146, 210, 209, 253, 172, 250, 325, 243, 294, 406, 365, 465, 16, 528, 561, 595, 402, 666, 665, 741, 372, 820, 673, 903, 726, 945, 897, 1081, 536, 1029, 1125, 1275, 1170, 1378, 765, 1485

Offset

1,3

Links

Sebastian Karlsson, Table of n, a(n) for n = 1..10000

Formula

a(n) = n*A010848(n)/2, if n is odd.

a(n) = n*(n-1)/2, if n is both odd and squarefree.

a(p^e) = (1/2)*(p-1)*p^(2*e-1), if p is an odd prime.

a(2^e) = 2^(e-1).

Maple

a:= n-> add(k&^n mod n, k=1..n-1):
seq(a(n), n=1..55);  # Alois P. Heinz, Feb 13 2021

Prog

(Python)
def a(n):
    return sum([pow(k, n, n) for k in range(1, n)])
for n in range(1, 56):
    print(a(n), end=', ')
(PARI) a(n) = sum(k=1, n-1, lift(Mod(k, n)^n)); \\ Michel Marcus, Jan 22 2021

Crossrefs

Cf. A010848, A048153, A048155, A094264, A121706, A195637, A195812, A202034.

Sequence in context: A064367 A113980 A095675 * A226442 A300374 A256063

Adjacent sequences: A340803 A340804 A340805 * A340807 A340808 A340809

Keyword

nonn

Author

Sebastian Karlsson, Jan 22 2021

Status

approved