A094264 -id:A094264 - cp's OEIS frontend

A094263 Triangle read by rows: for 1 <= k <= n, a(n, k) = n^k mod k.

0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 0, 0, 0, 2, 0, 3, 4, 1, 0, 0, 1, 0, 1, 4, 3, 2, 1, 0, 0, 0, 1, 0, 0, 4, 3, 0, 1, 0, 0, 1, 2, 1, 1, 1, 4, 1, 8, 1, 0, 0, 0, 0, 0, 2, 0, 5, 0, 0, 4, 1, 0, 0, 1, 1, 1, 3, 1, 6, 1, 1, 9, 2, 1, 0, 0, 0, 2, 0, 4, 4, 0, 0, 8, 6, 3, 4, 1, 0

Offset: 1

Amarnath Murthy, Apr 26 2004

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A094264, A094265.

Table[PowerMod[n,k,k],{n,20},{k,n}]//Flatten (* Harvey P. Dale, Apr 14 2020 *)

Edited and extended by David Wasserman, Jan 24 2007

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

Original entry on oeis.org

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

Sebastian Karlsson, Jan 22 2021

nonn

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

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

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

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

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=', ')

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).

cp's OEIS Frontend

A094263 Triangle read by rows: for 1 <= k <= n, a(n, k) = n^k mod k.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

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

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

PARI

Python

Formula