cp's OEIS Frontend

A333570 Number of nonnegative values c such that c^n == -c (mod n).

%I A333570 #34 Sep 08 2022 08:46:25
%S A333570 1,2,1,2,1,4,1,2,1,4,1,4,1,4,3,2,1,4,1,4,1,4,1,4,1,4,1,8,1,8,1,2,1,4,
%T A333570 3,4,1,4,3,4,1,8,1,4,1,4,1,4,1,4,3,8,1,4,3,4,1,4,1,8,1,4,1,2,1,24,1,4,
%U A333570 1,16,1,4,1,4,3,8,1,8,1,4,1,4,1,8,5,4,3,4,1,8,7,4,1,4,3
%N A333570 Number of nonnegative values c such that c^n == -c (mod n).
%C A333570 a(n) is the number of nonnegative bases c < n such that c^n + c == 0 (mod n).
%C A333570 a(2^k) = 2 for k > 0.
%C A333570 a(p^m) = 1 for odd prime p with m >= 0.
%C A333570 Let fy(n) = (the number of values b in Z/nZ such that b^y = b)/(the number of values c in Z/nZ such that -c^y = c) for nonnegative y, then:
%C A333570 f0(n) = A000012(n),
%C A333570 f1(n) = A026741(n),
%C A333570 f2(n) = A000012(n),
%C A333570 1 <= f3(n) <= n,
%C A333570 f4(n) = A000012(n), ...,
%C A333570 1 <= fn(n) = A182816(n)/a(n) <= n, where fn(n) = n for odd noncomposite numbers A006005 and Carmichael numbers A002997.
%H A333570 Antti Karttunen, <a href="/A333570/b333570.txt">Table of n, a(n) for n = 1..20000</a>
%F A333570 a(n) = A182816(n)/r for some odd r.
%o A333570 (Magma) [#[c: c in [0..n-1] | -c^n mod n eq c]: n in [1..95]];
%o A333570 (PARI) a(n) = sum(c=1, n, Mod(c, n)^n == -c); \\ _Michel Marcus_, Mar 27 2020
%Y A333570 Cf. A000012, A000079, A000961, A002997, A006005, A026741, A182816.
%K A333570 nonn
%O A333570 1,2
%A A333570 _Juri-Stepan Gerasimov_, Mar 27 2020