cp's OEIS Frontend

A337820 Array read by antidiagonals: T(n,k) (n >= 1, k >= 0) is the ratio (the number of nonnegative bases m < n such that m^k == m (mod n))/(the number of nonnegative bases m < n such that -m^k == m (mod n)).

%I A337820 #20 Sep 08 2022 08:46:25
%S A337820 1,1,1,1,1,1,1,3,1,1,1,2,1,1,1,1,5,1,3,1,1,1,3,1,3,1,1,1,1,7,1,1,1,3,
%T A337820 1,1,1,4,1,3,1,3,1,1,1,1,9,1,3,1,5,1,3,1,1,1,5,1,5,1,3,1,3,1,1,1,1,11,
%U A337820 1,3,1,3,1,1,1,3,1,1,1,6,1,1,1,5,1,3,1,3,1,1,1,1,13,1,3,1,3
%N A337820 Array read by antidiagonals: T(n,k) (n >= 1, k >= 0) is the ratio (the number of nonnegative bases m < n such that m^k == m (mod n))/(the number of nonnegative bases m < n such that -m^k == m (mod n)).
%C A337820 Array read by antidiagonals: T(n,k) (n >=1, k >= 0) is part of n of the form (the number of nonnegative bases m < n such that m^k == m (mod n))/(the number of nonnegative bases m < n such that -m^k == m (mod n)).
%F A337820 T(n, 2*k) = 1;  1 <= T(n, 2*k+1) <= n.
%e A337820 The initial rows of the array are:
%e A337820   1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A337820   1, 1, 3, 2, 5, 3, 7, 4, 9, 5, 11, 6, 13, ...
%e A337820   1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A337820   1, 1, 3, 3, 1, 3, 3, 5, 3, 1, 3, 9, 1, ...
%e A337820   1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A337820   1, 1, 3, 3, 5, 3, 3, 5, 3, 5, 3, 9, 5, ...
%e A337820   1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A337820   1, 1, 3, 3, 1, 3, 7, 5, 7, 1, 3, 9, 1, ...
%e A337820   1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A337820   1, 1, 3, 3, 5, 3, 3, 5, 3, 5, 3, 9, 5, ...
%e A337820   1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A337820   1, 1, 3, 3, 1, 3, 3, 5, 3, 1, 3, 9, 1, ...
%e A337820   1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A337820   1, 1, 3, 3, 5, 3, 7, 5, 7, 5, 3, 9, 5, ...
%e A337820 The initial antidiagonals are:
%e A337820      1,
%e A337820      1,  1,
%e A337820      1,  1, 1,
%e A337820      1,  3, 1, 1,
%e A337820      1,  2, 1, 1, 1,
%e A337820      1,  5, 1, 3, 1, 1,
%e A337820      1,  3, 1, 3, 1, 1, 1,
%e A337820      1,  7, 1, 1, 1, 3, 1, 1,
%e A337820      1,  4, 1, 3, 1, 3, 1, 1, 1,
%e A337820      1,  9, 1, 3, 1, 5, 1, 3, 1, 1,
%e A337820      1,  5, 1, 5, 1, 3, 1, 3, 1, 1, 1,
%e A337820      1, 11, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1,
%e A337820      1,  6, 1, 1, 1, 5, 1, 3, 1, 3, 1, 1, 1,
%e A337820      1, 13, 1, 3, 1, 3, 1, 7, 1, 5, 1, 3, 1, 1,
%e A337820 ...
%o A337820 (Magma) /* As triangle */ [[#[m: m in [0..n-k-1] | m^k mod (n-k) eq m]/
%o A337820 #[m: m in [0..n-k-1] | -m^k mod (n-k) eq m]: k in [0..n-1]]: n in [1..13]];
%Y A337820 Columns 0-2: A000012, A026741, A000012.
%Y A337820 Cf. A000010, A000012, A000027, A002322, A182816, A333570, A334006, A334597, A336664.
%K A337820 nonn,tabl
%O A337820 1,8
%A A337820 _Juri-Stepan Gerasimov_, Sep 23 2020