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!)
A137851 a(n) = A054525(n) * A061397(n). 5
0, 2, 3, -2, 5, -5, 7, 0, -3, -7, 11, 2, 13, -9, -8, 0, 17, 3, 19, 2, -10, -13, 23, 0, -5, -15, 0, 2, 29, 10, 31, 0, -14, -19, -12, 0, 37, -21, -16, 0, 41, 12, 43, 2, 3, -25, 47, 0, -7, 5, -20, 2, 53, 0, -16, 0, -22, -31, 59, -2, 61, -33, 3, 0, -18, 16, 67, 2, -26, 14, 71, 0, 73, -39, 5, 2, -18, 18, 79, 0, 0, -43, 83, -2, -22, -45, -32, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Equals row sums of triangle A143517. - Gary W. Adamson, Aug 22 2008
LINKS
FORMULA
A054525 * A061397 = Möbius transform of [0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 11, 0, 13, ...].
Dirichlet g.f.: primezeta(s-1)/zeta(s). - Benedict W. J. Irwin, Jul 11 2018
a(n) = Sum_{p|n} p*mu(n/p), where p is prime. - Ridouane Oudra, Nov 12 2019
EXAMPLE
a(4) = -2 = (0, -1, 0, 1) dot (0, 2, 3, 0), where (0, -1, 0, 1) = row 4 of the Möbius triangle A054525 and (0, 2, 3, 0) = the first 4 terms of A061397.
MAPLE
A061397 := proc(n) if isprime(n) then n; else 0 ; fi ; end: A054525 := proc(n, k) if n mod k = 0 then numtheory[mobius](n/k); else 0; fi ; end: A137851 := proc(n) local k ; add(A061397(k)* A054525(n, k), k=1..n) ; end: seq(A137851(n), n=1..120) ; # R. J. Mathar, May 23 2008
MATHEMATICA
a[n_] := If[n == 1, 0, With[{p = FactorInteger[n][[All, 1]]}, p*MoebiusMu[n/p] // Total]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jun 13 2023 *)
PROG
(Sage)
def A137851(n):
return add(d*moebius(n//d) for d in divisors(n) if is_prime(d))
[A137851(n) for n in (1..88)] # Peter Luschny, Feb 01 2012
CROSSREFS
Sequence in context: A330049 A240858 A035361 * A369742 A367476 A141346
KEYWORD
easy,sign
AUTHOR
Gary W. Adamson, Feb 14 2008
EXTENSIONS
More terms from R. J. Mathar, May 23 2008
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 28 04:02 EDT 2024. Contains 372900 sequences. (Running on oeis4.)