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 A220020 Number of cyclotomic cosets of 9 mod 10^n. 0
 6, 20, 56, 140, 256, 404, 584, 796, 1040, 1316, 1624, 1964, 2336, 2740, 3176, 3644, 4144, 4676, 5240, 5836, 6464, 7124, 7816, 8540, 9296, 10084, 10904, 11756, 12640, 13556, 14504, 15484, 16496, 17540, 18616, 19724, 20864, 22036, 23240, 24476, 25744, 27044, 28376, 29740, 31136, 32564, 34024, 35516, 37040, 38596 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..50. Index entries for linear recurrences with constant coefficients, signature (3, -3, 1). FORMULA Conjecture: a(n) = 4*(4*n^2-7*n-1) for n>2. a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>5. G.f.: 2*x*(8*x^4-13*x^3-7*x^2-x-3) / (x-1)^3. - Colin Barker, Apr 13 2013 EXAMPLE a(2) = 20 because there are 20 cyclotomic cosets of 9 mod 100: {1, 9, 81, 29, 61, 49, 41, 69, 21, 89} {3, 27, 43, 87, 83, 47, 23, 7, 63, 67} {11, 99, 91, 19, 71, 39, 51, 59, 31, 79} {13, 17, 53, 77, 93, 37, 33, 97, 73, 57} {2, 18, 62, 58, 22, 98, 82, 38, 42, 78} {4, 36, 24, 16, 44, 96, 64, 76, 84, 56} {6, 54, 86, 74, 66, 94, 46, 14, 26, 34} {8, 72, 48, 32, 88, 92, 28, 52, 68, 12} {10, 90} {30, 70} {20, 80} {40, 60} {50} {5, 45} {15, 35} {55, 95} {65, 85} {25} {75} {0} MATHEMATICA a[n_] := DivisorSum[10^n, EulerPhi[#]/MultiplicativeOrder[9, #]&]; Array[a, 50] (* Jean-François Alcover, Dec 10 2015, adapted from PARI *) PROG (PARI) for(n=1, 50, print1(sumdiv(10^n, d, eulerphi(d)/znorder(Mod(9, d)))", ")) CROSSREFS Cf. A006694, A220468. Sequence in context: A109903 A323640 A249406 * A201149 A260777 A014480 Adjacent sequences: A220017 A220018 A220019 * A220021 A220022 A220023 KEYWORD base,nonn AUTHOR V. Raman, Jan 27 2013 STATUS approved

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Last modified July 15 22:54 EDT 2024. Contains 374334 sequences. (Running on oeis4.)