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

1,5

Links

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

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)

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 *)

Prog

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

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.

Sequence in context: A275622 A129239 A224825 * A290794 A328178 A127571

Adjacent sequences: A341410 A341411 A341412 * A341414 A341415 A341416

Keyword

nonn

Author

Seiichi Manyama, Feb 11 2021

Status

approved