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 A280196 Numbers n such that a^(n-1) == 1 (mod n^2) has no solutions with 1 < a < n^2-1. 2
 1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 27, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 54, 56, 58, 60, 62, 64, 68, 72, 74, 78, 80, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 114, 116, 118, 120, 122, 126, 128, 132, 134, 136, 138 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 1 and numbers n such that A185103(n) = n^2 + (-1)^n. Complement of A280199. Union of A000244 and A209211. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE a(4) = 4 is in the sequence because a^3 == 1 (mod 4^2) has no solutions except a == 1 (mod 4^2). a(7) = 9 is in the sequence because a^8 == 1 (mod 9^2) has no solutions except a == 1 (mod 9^2) and a == 80 (mod 9^2), and 80 = 9^2-1. MAPLE Aeven:= select(t -> igcd(t-1, numtheory:-phi(t^2))=1, {seq(i, i=2..1000, 2}}): Aodd:= {seq(3^i, i=0..floor(log[3](1000)))}: sort(convert(Aeven union Aodd, list)); MATHEMATICA Aeven = Select[Range[2, 1000, 2], GCD[#-1, EulerPhi[#^2]] == 1&]; Aodd = 3^Range[0, Floor[Log[3, 1000]]]; Union[Aeven, Aodd] (* Jean-François Alcover, Apr 27 2019, from Maple *) CROSSREFS Cf. A000244, A185103, A209211, A280199. Sequence in context: A054219 A196277 A368385 * A143896 A160719 A263079 Adjacent sequences: A280193 A280194 A280195 * A280197 A280198 A280199 KEYWORD nonn AUTHOR Robert Israel and Thomas Ordowski, Dec 28 2016 STATUS approved

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Last modified August 15 04:20 EDT 2024. Contains 375172 sequences. (Running on oeis4.)