A385540 Number of values of nonnegative s < n such that s^s == (-s)^s == s (mod n).
1, 1, 0, 0, 0, 2, 1, 0, 1, 2, 0, 1, 0, 3, 2, 0, 0, 4, 0, 1, 2, 3, 1, 1, 2, 4, 1, 3, 0, 4, 1, 0, 3, 2, 1, 3, 1, 3, 2, 1, 1, 6, 0, 3, 4, 3, 1, 1, 3, 6, 2, 2, 0, 4, 3, 2, 1, 3, 0, 3, 1, 3, 7, 0, 3, 6, 0, 1, 3, 6, 1, 3, 1, 4, 5, 3, 4, 6, 1, 1, 4, 3, 0, 5, 0, 4, 4, 2, 1, 8, 4, 2, 3, 3, 2, 1, 0, 8, 5, 5
Offset: 1
Keywords
Programs
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Magma
[#[s: s in [0..n-1] | Modexp(s,s,n) eq s and Modexp(-s,s,n) eq s]: n in [1..100]];
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Mathematica
a[n_] := Count[Range[0, n-1], ?(PowerMod[#, #, n] == PowerMod[-#, #, n] == # &)]; Array[a, 100] (* _Amiram Eldar, Jul 03 2025 *)
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PARI
a(n) = sum(s=0, n-1, (s == Mod(s, n)^s) && (s == Mod(-s, n)^s)); \\ Michel Marcus, Jul 09 2025