A390392 - OEIS

%I #10 Nov 11 2025 21:43:41

%S 1,2,30,390,6270,36894,528990,6373290,32222190,3180844590,2248482390

%N Smallest k for which the number of divisors d of k such that d == -d^(k/d) (mod k) is equal to n, or -1 if no such k exists.

%o (Magma) [Min([k: k in [1..5*10^5] | 1 + #[d: d in Divisors(k) | -Modexp(d, k div d, k) mod k eq d] eq n]): n in [1..6]];

%o (PARI) f(k) = sumdiv(k, d, -Mod(d, k)^(k/d) == d);

%o list(len) = {my(v = vector(len), c = 0, k = 1, i); while(c < len, i = f(k); if(i <= len && v[i] == 0, c++; v[i] = k); k++); v;} \\ _Amiram Eldar_, Nov 06 2025

%Y Cf. A386913.

%K nonn,more

%O 1,2

%A _Juri-Stepan Gerasimov_, Nov 03 2025

%E a(10)-a(11) from _Amiram Eldar_, Nov 06 2025