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 A220019 Number of cyclotomic cosets of 7 mod 10^n. 0
 4, 27, 93, 265, 685, 1265, 2005, 2905, 3965, 5185, 6565, 8105, 9805, 11665, 13685, 15865, 18205, 20705, 23365, 26185, 29165, 32305, 35605, 39065, 42685, 46465, 50405, 54505, 58765, 63185, 67765, 72505, 77405, 82465, 87685, 93065, 98605, 104305, 110165, 116185, 122365, 128705, 135205, 141865, 148685 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS FORMULA Empirical G.f.: x*(88*x^5-142*x^4-63*x^3-24*x^2-15*x-4) / (x-1)^3. [Colin Barker, Feb 03 2013] Conjecture: a(n) = 5*(16*n^2-60*n+37) for n>3. a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>6. [Colin Barker, Apr 14 2013] EXAMPLE a(2) = 27 because there are 27 cyclotomic cosets of 7 mod 100: {1, 7, 49, 43} {2, 14, 98, 86} {3, 21, 47, 29} {4, 28, 96, 72} {5, 35, 45, 15} {6, 42, 94, 58} {8, 56, 92, 44} {9, 63, 41, 87} {10, 70, 90, 30} {11, 77, 39, 73} {12, 84, 88, 16} {13, 91, 37, 59} {17, 19, 33, 31} {18, 26, 82, 74} {20, 40, 80, 60} {22, 54, 78, 46} {23, 61, 27, 89} {24, 68, 76, 32} {25, 75} {34, 38, 66, 62} {36, 52, 64, 48} {50} {51, 57, 99, 93} {53, 71, 97, 79} {55, 85, 95, 65} {67, 69, 83, 81} {0} MATHEMATICA a[n_] := DivisorSum[10^n, EulerPhi[#] / MultiplicativeOrder[7, #] & ]; Array[a, 50] (* Jean-François Alcover, Dec 18 2015 *) PROG (PARI) for(n=1, 50, print1(sumdiv(10^n, d, eulerphi(d)/znorder(Mod(7, d)))", ")) CROSSREFS Cf. A006694, A220468. Sequence in context: A298987 A070600 A100488 * A225902 A071174 A092364 Adjacent sequences:  A220016 A220017 A220018 * A220020 A220021 A220022 KEYWORD base,nonn AUTHOR V. Raman, Jan 27 2013 STATUS approved

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Last modified May 26 17:16 EDT 2022. Contains 354092 sequences. (Running on oeis4.)