login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A209198 a(n) = 1 if n not == 2 (mod 4) and relatively prime to 63 otherwise 0. 2
1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
G.f.: B(x) - B(x^7) - B(x^9) + B(x^63) where B(x) = (x + x^3 + x^4) / (1 - x^4).
a(n) is multiplicative with a(2^e) = 1 if e!=1, a(3^e) = 1 if e<2, a(7^e) = 0^e, a(p^e) = 1 otherwise.
a(n) = a(n + 252) = a(-n), a(4*n + 2) = a(7*n) = a(9*n) = 0 for all n in Z.
Euler transform is A119952.
From Amiram Eldar, Oct 24 2023: (Start)
Dirichlet g.f.: zeta(s) * (1 - 1/2^s + 1/4^s) * (1 - 1/9^s) * (1 - 1/7^s).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4/7. (End)
EXAMPLE
G.f. = x + x^3 + x^4 + x^5 + x^8 + x^11 + x^12 + x^13 + x^15 + x^16 + x^17 + ...
MATHEMATICA
B[x_]:= (x + x^3 + x^4)/(1 - x^4); CoefficientList[Series[B[x] - B[x^7] - B[x^9] + B[x^63], {x, 0, 50}], x] (* G. C. Greubel, Aug 11 2018 *)
PROG
(PARI) {a(n) = my(A, p, e); n = abs(n); if( n<1, 0, A = factor(n); prod( k=1, matsize(A)[1], [p, e] = A[k, ]; if( p==2, e>1, p==3, e<2, p==7, 0, 1)))};
(PARI) {a(n) = b(n) - b(n/7) - b(n/9) + b(n/63)}; {b(n) = if( n == round(n), n%4 != 2, 0)};
(PARI) {a(n) = n%4!=2 && n%7!=0 && n%9!=0};
CROSSREFS
Cf. A119952.
Sequence in context: A230298 A000480 A118251 * A282343 A099076 A282339
KEYWORD
nonn,easy,mult
AUTHOR
Michael Somos, Mar 05 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)