A385541 -id:A385541 - cp's OEIS frontend

A386410 Smallest k for which A385541(k) = n.

1, 2, 66, 30, 1386, 858, 34650, 1287678, 6380946, 11411400, 24877650

Offset: 1

Juri-Stepan Gerasimov, Jul 21 2025

A386410[n_] := DivisorSum[n, 1 &, PowerMod[#, #, n] == PowerMod[-#, #, n] == Mod[#, n] &]; seq[lim_] := Module[{s = Array[A386410, lim]}, TakeWhile[Flatten[FirstPosition[s, #] & /@ Range[Max[s]]], !MissingQ[#] &]]; seq[10^5] (* Amiram Eldar, Jul 21 2025 *)

a(8)-a(11) from Amiram Eldar, Jul 21 2025

A385540 Number of values of nonnegative s < n such that s^s == (-s)^s == s (mod n).

Original entry on oeis.org

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

Juri-Stepan Gerasimov, Jul 02 2025

nonn

Cf. A065295, A384781, A385541.

[#[s: s in [0..n-1] | Modexp(s,s,n) eq s and Modexp(-s,s,n) eq s]: n in [1..100]];

a[n_] := Count[Range[0, n-1], ?(PowerMod[#, #, n] == PowerMod[-#, #, n] == # &)]; Array[a, 100] (* _Amiram Eldar, Jul 03 2025 *)

a(n) = sum(s=0, n-1, (s == Mod(s, n)^s) && (s == Mod(-s, n)^s)); \\ Michel Marcus, Jul 09 2025

cp's OEIS Frontend

A386410 Smallest k for which A385541(k) = n.

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