OFFSET
1,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).
FORMULA
a(n) = A220018(n) for n = 1.
a(n) = A220018(n) + 1 for all n >= 2.
Conjecture: a(n) = 2*n*(4*n-7) for n>2. a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>5. G.f.: 2*x*(4*x^4-7*x^3-3*x^2-2) / (x-1)^3. - Colin Barker, Apr 14 2013
EXAMPLE
a(2) = 12 because there are 12 cyclotomic cosets of 13 mod 100:
{1, 13, 69, 97, 61, 93, 9, 17, 21, 73, 49, 37, 81, 53, 89, 57, 41, 33, 29, 77}
{3, 39, 7, 91, 83, 79, 27, 51, 63, 19, 47, 11, 43, 59, 67, 71, 23, 99, 87, 31}
{2, 26, 38, 94, 22, 86, 18, 34, 42, 46, 98, 74, 62, 6, 78, 14, 82, 66, 58, 54}
{4, 52, 76, 88, 44, 72, 36, 68, 84, 92, 96, 48, 24, 12, 56, 28, 64, 32, 16, 8}
{5, 65, 45, 85}
{15, 95, 35, 55}
{25}
{75}
{10, 30, 90, 70}
{20, 60, 80, 40}
{50}
{0}
MATHEMATICA
a[n_]:=DivisorSum[10^n, EulerPhi[#]/MultiplicativeOrder[13, #]&]; Array[a, 50] (* Ray Chandler, Jul 03 2023, after Jean-François Alcover *)
PROG
(PARI) for(n=1, 50, print1(sumdiv(10^n, d, eulerphi(d)/znorder(Mod(13, d)))", "))
CROSSREFS
KEYWORD
base,nonn
AUTHOR
V. Raman, Jan 28 2013
STATUS
approved