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A279680 Definition: m < n is an extradivisor of n if for some positive k < n, m | n | k^(n+1) + m and n | (n-k)^(n+1) + m. This sequence gives the smallest number with n extradivisors.

%I A279680 #16 Jun 19 2020 03:55:34
%S A279680 1,2,45,105,1365,1305,4305,11445
%N A279680 Definition: m < n is an extradivisor of n if for some positive k < n, m | n | k^(n+1) + m and n | (n-k)^(n+1) + m. This sequence gives the smallest number with n extradivisors.
%e A279680 a(0) = 1 with extradivisors {};
%e A279680 a(1) = 2 with extradivisor {1};
%e A279680 a(2) = 45 with extradivisors {5, 9};
%e A279680 a(3) = 105 with extradivisors {5, 21, 35};
%e A279680 a(4) = 1365 with extradivisors {35, 105, 195, 455};
%e A279680 a(5) = 1305 with extradivisors {5, 9, 29, 45, 261}.
%t A279680 First /@ Values@ KeySort@ PositionIndex@ Table[Count[DeleteCases[Most@ Divisors@ n, d_ /; EvenQ@ d], m_ /; Total@ Boole@ Map[Function[k, And[Mod[PowerMod[k, (n + 1), n] + m, n] == 0, Mod[PowerMod[(n - k), (n + 1), n] + m, n] == 0]], Range[n - 1]] > 0], {n, 1500}] (* _Michael De Vlieger_, Dec 17 2016, Version 10 *)
%Y A279680 Cf. A272538, A279024.
%K A279680 nonn,more
%O A279680 0,2
%A A279680 _Juri-Stepan Gerasimov_, Dec 16 2016
%E A279680 a(3)-a(7) from _Michael De Vlieger_, Dec 07 2016
%E A279680 Definition edited by _N. J. A. Sloane_, Jun 19 2020