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!)
A100007 Number of unitary divisors of 2n-1 (d such that d divides 2n-1, GCD(d,(2n-1)/d)=1). Bisection of A034444. 2
1, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 2, 4, 4, 2, 4, 2, 2, 4, 2, 2, 4, 2, 4, 4, 2, 2, 4, 4, 2, 4, 2, 2, 4, 4, 2, 2, 2, 4, 4, 2, 4, 4, 4, 2, 4, 2, 2, 8, 2, 2, 4, 2, 4, 4, 4, 2, 4, 2, 2, 4, 2, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 4, 4, 2, 4, 4, 2, 8, 2, 2, 4, 2, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 8, 2, 2, 4, 4, 4, 4, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
From Ilya Gutkovskiy, Apr 28 2017: (Start)
a(n) = [x^(2*n-1)] Sum_{k>=1} mu(k)^2*x^k/(1 - x^k).
a(n) = 2^omega(2*n-1). (End)
From Amiram Eldar, Jan 28 2023: (Start)
a(n) = A034444(2*n-1) = A068068(2*n-1).
Sum_{k=1..n} a(k) ~ 4*n*((log(n) + 2*gamma - 1 + 7*log(2)/3 - 2*zeta'(2)/zeta(2)) / Pi^2, where gamma is Euler's constant (A001620). (End)
EXAMPLE
a(13)=2 because among the three divisors of 25 only 1 and 25 are unitary.
MAPLE
with(numtheory): for n from 1 to 120 do printf(`%d, `, 2^nops(ifactors(2*n-1)[2])) od: # Emeric Deutsch, Dec 24 2004
MATHEMATICA
a[n_] := 2^PrimeNu[2*n-1]; Array[a, 100] (* Amiram Eldar, Jan 28 2023 *)
PROG
(PARI) a(n) = 2^omega(2*n-1); \\ Amiram Eldar, Jan 28 2023
CROSSREFS
Sequence in context: A083261 A003648 A003642 * A104369 A051702 A073130
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 20 2004
EXTENSIONS
More terms from Emeric Deutsch, Dec 24 2004
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 February 29 21:35 EST 2024. Contains 370428 sequences. (Running on oeis4.)