The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A005089 Number of distinct primes == 1 (mod 4) dividing n. 10
0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,65
LINKS
Étienne Fouvry and Peter Koymans, On Dirichlet biquadratic fields, arXiv:2001.05350 [math.NT], 2020.
FORMULA
Additive with a(p^e) = 1 if p == 1 (mod 4), 0 otherwise.
From Reinhard Zumkeller, Jan 07 2013: (Start)
a(n) = Sum_{k=1..A001221(n)} A079260(A027748(n,k)).
a(A004144(n)) = 0.
a(A009003(n)) > 0. (End)
MAPLE
A005089 := proc(n)
local a, pe;
a := 0 ;
for pe in ifactors(n)[2] do
if modp(op(1, pe), 4) =1 then
a := a+1 ;
end if;
end do:
a ;
end proc:
seq(A005089(n), n=1..100) ; # R. J. Mathar, Jul 22 2021
MATHEMATICA
f[n_]:=Length@Select[If[n==1, {}, FactorInteger[n]], Mod[#[[1]], 4]==1&]; Table[f[n], {n, 102}] (* Ray Chandler, Dec 18 2011 *)
a[n_] := DivisorSum[n, Boole[PrimeQ[#] && Mod[#, 4] == 1]&]; Array[a, 100] (* Jean-François Alcover, Dec 01 2015 *)
PROG
(PARI) for(n=1, 100, print1(sumdiv(n, d, isprime(d)*if((d-1)%4, 0, 1)), ", "))
(Haskell)
a005089 = sum . map a079260 . a027748_row
-- Reinhard Zumkeller, Jan 07 2013
(Magma) [#[p:p in PrimeDivisors(n)|p mod 4 eq 1]: n in [1..100]]; // Marius A. Burtea, Jan 16 2020
CROSSREFS
Sequence in context: A320005 A325414 A216510 * A364127 A340999 A119395
KEYWORD
nonn
AUTHOR
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 May 18 09:54 EDT 2024. Contains 372620 sequences. (Running on oeis4.)