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!)
A143275 A054525 * A029935. 1
1, 1, 3, 3, 7, 3, 11, 7, 12, 7, 19, 9, 23, 11, 21, 16, 31, 12, 35, 21, 33, 19, 43, 21, 48, 23, 44, 33, 55, 21, 59, 36, 57, 31, 77, 36, 71, 35, 69, 49, 79, 33, 83, 57, 84, 43, 91, 48, 108, 48, 93, 69, 103, 44, 133, 77, 105, 55, 115, 63, 119, 59, 132, 80, 161, 57, 131, 93, 129 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
Möbius transform (A054525) of A029935: (1, 2, 4, 5, 8, 8, 12, 12, 16, ...).
Multiplicative with a(p) = 2*p - 3 and a(p^e) = (e*(p-1) + p + 2) * (p-1)^2 * p^(e-3) for e > 1. - Amiram Eldar, Aug 31 2023
EXAMPLE
a(4) = 3 = (0, -1, 0, 1) dot (1, 2, 4, 5) = (0 - 2 + 0 + 5), where K(0, -1, 0, 1) = row 4 of A054525 and A143275 = (1, 2, 4, 5, 8, 8, 12, ...).
MAPLE
read("transforms") : A029935 := proc(n) local a, d ; a := 0 ; for d in numtheory[divisors](n) do a := a+ numtheory[phi](d)*numtheory[phi](n/d); od; RETURN(a) ; end: a029935 := [seq(A029935(n), n=1..300)] ; a143275 := MOBIUS(a029935) ; # R. J. Mathar, Jan 19 2009
MATHEMATICA
f[p_, e_] := If[e > 1, (e*(p-1) + p + 2) * (p-1)^2 * p^(e-3), 2*p - 3]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 31 2023 *)
CROSSREFS
Sequence in context: A164928 A253249 A069949 * A083262 A122978 A119347
KEYWORD
nonn,easy,mult
AUTHOR
Gary W. Adamson, Aug 03 2008
EXTENSIONS
More terms from R. J. Mathar, Jan 19 2009
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 21 07:02 EDT 2024. Contains 372729 sequences. (Running on oeis4.)