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

Author

Sebastian Karlsson, Jan 22 2021

Keywords

• nonn

Links

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

Crossrefs

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

Programs

Maple

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

PARI

a(n) = sum(k=1, n-1, lift(Mod(k, n)^n)); \\ Michel Marcus, Jan 22 2021

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=', ')

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).