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

%I #40 Sep 25 2025 22:20:58

%S 1,2,6,42,66,1770,2926,8646,178486,90706,639730,17646706,5533066,

%T 35193246,13775230,144313246

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

%o (Magma) [Min([k: k in [1..2*10^5] | 1 + #[d: d in Divisors(k) | -Modexp(d,k,k) mod k eq d] eq n]): n in [1..10]];

%Y Cf. A032741, A371513, A380393, A380656.

%K nonn,more

%O 0,2

%A _Juri-Stepan Gerasimov_, Sep 05 2025