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!)
A327626 Expansion of Sum_{k>=1} x^(k^3) / (1 - x^(k^3))^2. 2
1, 2, 3, 4, 5, 6, 7, 9, 9, 10, 11, 12, 13, 14, 15, 18, 17, 18, 19, 20, 21, 22, 23, 27, 25, 26, 28, 28, 29, 30, 31, 36, 33, 34, 35, 36, 37, 38, 39, 45, 41, 42, 43, 44, 45, 46, 47, 54, 49, 50, 51, 52, 53, 56, 55, 63, 57, 58, 59, 60, 61, 62, 63, 73, 65, 66, 67, 68, 69, 70, 71, 81, 73, 74, 75 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Sum of divisors d of n such that n/d is a cube.
Inverse Moebius transform of A078429.
LINKS
FORMULA
a(n) = Sum_{d|n} A078429(d).
a(n) = Sum_{d|n} A010057(n/d) * d. Dirichlet convolution of A000027 and A010057.
D.g.f.: zeta(s-1)*zeta(3s). - R. J. Mathar, Jun 05 2020
Sum_{k=1..n} a(k) ~ Pi^6 * n^2 / 1890. - Vaclav Kotesovec, May 20 2021
MATHEMATICA
nmax = 75; CoefficientList[Series[Sum[x^(k^3)/(1 - x^(k^3))^2, {k, 1, Floor[nmax^(1/3)] + 1}], {x, 0, nmax}], x] // Rest
a[n_] := DivisorSum[n, # &, IntegerQ[(n/#)^(1/3)] &]; Table[a[n], {n, 1, 75}]
PROG
(PARI) A327626(n) = sumdiv(n, d, ispower(n/d, 3)*d); \\ Antti Karttunen, Sep 19 2019
CROSSREFS
Sequence in context: A284049 A063932 A323785 * A179464 A071191 A300903
KEYWORD
nonn,mult
AUTHOR
Ilya Gutkovskiy, Sep 19 2019
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 March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)