|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
LINKS
|
|
|
FORMULA
|
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:
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|