# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a341413 Showing 1-1 of 1 %I A341413 #19 Feb 10 2023 12:53:40 %S A341413 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, %T A341413 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, %U A341413 28,43,24,28,56,28,16,28,4,18,20,28,52,25,0,28,68,28,66,19,40 %N A341413 a(n) = (Sum_{k=1..7} k^n) mod n. %H A341413 Robert Israel, Table of n, a(n) for n = 1..10000 %F A341413 a(n) = A001554(n) mod n. %F A341413 a(A056750(n)) = 0. %F A341413 From _Robert Israel_, Feb 09 2023: (Start) %F A341413 Given positive integer k, let m = A001554(k). %F A341413 If p is a prime > m/k and A001554(p*k) == m (mod k), then a(p*k) = m. %F A341413 This is true for all primes p > m/k for k = 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 14, ... %F A341413 For k = 5 or 15 it is true for primes p > m/k with p == 1 (mod 4). %F A341413 For k = 11 it is true for primes p > m/k with p == 1 or 7 (mod 10). %F A341413 For k = 13 it is true for primes p > m/k with p == 1 (mod 12). %F A341413 (End) %p A341413 a:= n-> add(i&^n, i=1..7) mod n: %p A341413 seq(a(n), n=1..100); # _Alois P. Heinz_, Feb 11 2021 %t A341413 a[n_] := Mod[Sum[k^n, {k, 1, 7}], n]; Array[a, 100] (* _Amiram Eldar_, Feb 11 2021 *) %o A341413 (PARI) a(n) = sum(k=1, 7, k^n)%n; %Y A341413 (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). %Y A341413 Cf. A001554, A056750. %K A341413 nonn %O A341413 1,5 %A A341413 _Seiichi Manyama_, Feb 11 2021 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE