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A290542 a(n) is the least integer k in the interval [2, sqrt(n)] such that k^n == k (mod n), or 0 if no such integer exists.

%I A290542 #25 Sep 08 2022 08:46:19
%S A290542 0,2,0,2,0,0,0,2,0,2,0,0,0,2,0,2,0,0,0,2,0,0,0,0,4,2,0,2,0,0,0,0,0,2,
%T A290542 0,0,0,2,0,2,0,0,0,2,0,0,0,0,0,2,0,0,0,0,0,2,0,2,0,0,0,5,3,2,0,0,0,2,
%U A290542 0,2,0,0,0,0,0,2,0,0,0,2,0,4,0,0,0,2,0
%N A290542 a(n) is the least integer k in the interval [2, sqrt(n)] such that k^n == k (mod n), or 0 if no such integer exists.
%H A290542 Antti Karttunen, <a href="/A290542/b290542.txt">Table of n, a(n) for n = 4..20000</a>
%F A290542 a(A000040(n)) = 2 for n >= 3.
%F A290542 a(A001567(n)) = 2 for n >= 1.
%F A290542 a(A006935(n)) = 2 for n >= 2.
%F A290542 For n >= 3, a(x) = 2*A010051(x), where x = A000040(n).
%t A290542 Table[SelectFirst[Range[2, Sqrt@ n], PowerMod[#, n , n] == Mod[#, n] &] /. k_ /; MissingQ@ k -> 0, {n, 4, 90}] (* _Michael De Vlieger_, Aug 09 2017 *)
%o A290542 (Magma) lst:=[]; for n in [4..90] do r:=Floor(Sqrt(n)); for k in [2..r] do if Modexp(k, n, n) eq k then Append(~lst, k); break; end if; if k eq r then Append(~lst, 0); end if; end for; end for; lst;
%o A290542 (PARI) a(n) = for (k=2, sqrtint(n), if (Mod(k, n)^n == k, return(k));); return (0); \\ _Michel Marcus_, Aug 19 2017
%Y A290542 Cf. A010051, A290543.
%K A290542 nonn
%O A290542 4,2
%A A290542 _Arkadiusz Wesolowski_, Aug 05 2017