A341413 a(n) = (Sum_{k=1..7} k^n) mod n.

0, 0, 1, 0, 3, 2, 0, 4, 1, 0, 6, 8, 2, 0, 4, 4, 11, 14, 9, 16, 7, 8, 5, 20, 8, 10, 1, 0, 28, 20, 28, 4, 25, 4, 14, 32, 28, 26, 4, 36, 28, 20, 28, 12, 28, 2, 28, 20, 0, 0, 19, 48, 28, 32, 34, 28, 43, 24, 28, 56, 28, 16, 28, 4, 18, 20, 28, 52, 25, 0, 28, 68, 28, 66, 19, 40

Offset: 1

Author

Seiichi Manyama, Feb 11 2021

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

(Sum_{k=1..m} k^n) mod n: A096196 (m=2), A341409 (m=3), A341410 (m=4), A341411 (m=5), A341412 (m=6), this sequence (m=7).

Cf. A001554, A056750.

Programs

Maple

a:= n-> add(i&^n, i=1..7) mod n:
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 11 2021

Mathematica

a[n_] := Mod[Sum[k^n, {k, 1, 7}], n]; Array[a, 100] (* Amiram Eldar, Feb 11 2021 *)

PARI

a(n) = sum(k=1, 7, k^n)%n;

Formula

a(n) = A001554(n) mod n.

a(A056750(n)) = 0.

From Robert Israel, Feb 09 2023: (Start)

Given positive integer k, let m = A001554(k).

If p is a prime > m/k and A001554(p*k) == m (mod k), then a(p*k) = m.

This is true for all primes p > m/k for k = 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 14, ...

For k = 5 or 15 it is true for primes p > m/k with p == 1 (mod 4).

For k = 11 it is true for primes p > m/k with p == 1 or 7 (mod 10).

For k = 13 it is true for primes p > m/k with p == 1 (mod 12).

(End)