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!)
A284059 The absolute values of A275966. 1
1, 1, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 0, 2, 4, 0, 0, 4, 2, 0, 4, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
This is multiplicative function with a(p^n) = |Re(I^(p^n+1) - I^(p^(n-1)+1))|.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = |Re(I*Sum_{d|n}(mobius(d)*I^(n/d)))|.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3/Pi = 0.954929... (A089491). - Amiram Eldar, Jan 27 2024
EXAMPLE
a(9) = |Re(I*(mobius(1)*I^9 + mobius(3)*I^3 + mobius(9)*I))| = |Re((I^10 - I^4))| = |-2| = 2.
MAPLE
a(n):=abs(Re(I*add(numtheory:-mobius(d)*I^(n/d), d = numtheory:-divisors(n)))).
MATHEMATICA
Table[Abs@ Re[I* Sum[MoebiusMu[d] * I^(n/d), {d, Divisors[n]}]], {n, 87}] (* Indranil Ghosh, Mar 19 2017 *)
f[p_, e_] := If[Mod[p, 4] == 1, 0, 2]; f[2, e_] := If[e == 1, 1, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 27 2024 *)
PROG
(PARI) a(n)=my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]==2, if(f[i, 2]==1, 1, 0), if(f[i, 1]%4==3, 2, 0))) \\ Charles R Greathouse IV, Mar 22 2017
CROSSREFS
Sequence in context: A144734 A029361 A275966 * A329767 A356018 A107502
KEYWORD
nonn,mult
AUTHOR
Gevorg Hmayakyan, Mar 19 2017
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 July 12 11:20 EDT 2024. Contains 374244 sequences. (Running on oeis4.)