A048155 -id:A048155 - cp's OEIS frontend

A048154 Triangular array T read by rows: T(n,k)=k^3 mod n, for k=1,2,...,n, n=1,2,...

0, 1, 0, 1, 2, 0, 1, 0, 3, 0, 1, 3, 2, 4, 0, 1, 2, 3, 4, 5, 0, 1, 1, 6, 1, 6, 6, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0

Offset: 1

Clark Kimberling

			Rows:
{0};
{1, 0};
{1, 2, 0};
{1, 0, 3, 0};
{1, 3, 2, 4, 0};
{1, 2, 3, 4, 5, 0};
...

T. D. Noe, Rows n=1..100 of triangle, flattened

Cf. A048155.

Table[Mod[k^3, n], {n, 13}, {k, n}] // Flatten (* Michael De Vlieger, Jun 26 2016 *)

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

A048154 Triangular array T read by rows: T(n,k)=k^3 mod n, for k=1,2,...,n, n=1,2,...

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

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