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A341413
a(n) = (Sum_{k=1..7} k^n) mod n.
5
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
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).
Sequence in context: A275622 A129239 A224825 * A290794 A328178 A127571
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 11 2021
STATUS
approved