|
|
A091685
|
|
Sieve out 6n+1 and 6n-1.
|
|
1
|
|
|
0, 1, 0, 0, 0, 5, 0, 7, 0, 0, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 0, 0, 23, 0, 25, 0, 0, 0, 29, 0, 31, 0, 0, 0, 35, 0, 37, 0, 0, 0, 41, 0, 43, 0, 0, 0, 47, 0, 49, 0, 0, 0, 53, 0, 55, 0, 0, 0, 59, 0, 61, 0, 0, 0, 65, 0, 67, 0, 0, 0, 71, 0, 73, 0, 0, 0, 77, 0, 79, 0, 0, 0, 83, 0, 85, 0, 0, 0, 89, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
COMMENTS
|
Completely multiplicative with a(2) = a(3) = 0, a(p) = p otherwise. - David W. Wilson, Jun 12 2005
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2,0,0,0,0,0,-1).
|
|
FORMULA
|
a(n) = -Product_{k=0..5} Sum_{j=1..n} w(6)^(kj), w(6) = e^(2*Pi*i/6), i = sqrt(-1).
G.f.: x*(x^2+1)*(x^8-x^6+6*x^4-x^2+1) / ( (x-1)^2 *(1+x)^2 *(1+x+x^2)^2 *(x^2-x+1)^2 ). - R. J. Mathar, Feb 14 2015
Dirichlet g.f.: zeta(s-1) * (1 - 1/2^(s-1)) * (1 - 1/3^(s-1)).
Sum_{k=1..n} a(k) ~ n^2/6. (End)
|
|
MATHEMATICA
|
Table[n Boole[Or[# == 1, # == 5] &@ Mod[n, 6]], {n, 0, 90}] (* or *)
CoefficientList[Series[x (x^2 + 1) (x^8 - x^6 + 6 x^4 - x^2 + 1)/((x - 1)^2*(1 + x)^2*(1 + x + x^2)^2*(x^2 - x + 1)^2), {x, 0, 90}], x] (* Michael De Vlieger, Jul 24 2017 *)
|
|
PROG
|
(Python)
from sympy import gcd
def a(n): return n if gcd(n, 6) == 1 else 0
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|