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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. 1
 1, 2, 45, 105, 1365, 1305, 4305, 11445 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS EXAMPLE a(0) = 1 with extradivisors {}; a(1) = 2 with extradivisor {1}; a(2) = 45 with extradivisors {5, 9}; a(3) = 105 with extradivisors {5, 21, 35}; a(4) = 1365 with extradivisors {35, 105, 195, 455}; a(5) = 1305 with extradivisors {5, 9, 29, 45, 261}. MATHEMATICA 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 *) CROSSREFS Cf. A272538, A279024. Sequence in context: A343424 A041241 A304015 * A305363 A304955 A316637 Adjacent sequences:  A279677 A279678 A279679 * A279681 A279682 A279683 KEYWORD nonn,more AUTHOR Juri-Stepan Gerasimov, Dec 16 2016 EXTENSIONS a(3)-a(7) from Michael De Vlieger, Dec 07 2016 Definition edited by N. J. A. Sloane, Jun 19 2020 STATUS approved

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Last modified May 24 22:34 EDT 2022. Contains 354047 sequences. (Running on oeis4.)