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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

Table of n, a(n) for n=1..45.

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-Fran├žois 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.)