login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A061704 Number of cubes dividing n. 16
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Multiplicative with a(p^e) = floor(e/3) + 1. - Mitch Harris, Apr 19 2005

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

FORMULA

G.f.: Sum_{n>=1} x^(n^3)/(1-x^(n^3)). - Joerg Arndt, Jan 30 2011

a(n) = A000005(A053150(n)).

Dirichlet g.f.: zeta(3*s)*zeta(s). - Geoffrey Critzer, Feb 07 2015

EXAMPLE

a(128) = 4 since 128 is divisible by 1^3 = 1, 2^3 = 8 and 4^3 = 64.

MAPLE

N:= 1000: # to get a(1)..a(N)

G:= add(x^(n^3)/(1-x^(n^3)), n=1..floor(N^(1/3))):

S:= series(G, x, N+1):

seq(coeff(S, x, j), j=1..N); # Robert Israel, Jul 28 2017

MATHEMATICA

nn = 100; f[list_, i_]:= list[[i]]; Table[ DirichletConvolve[ f[ Boole[ Map[ IntegerQ[#] &, Map[#^(1/3) &, Range[nn]]]], n], f[Table[1, {nn}], n], n, m], {m, 1, nn}] (* Geoffrey Critzer, Feb 07 2015 *)

Table[DivisorSum[n, 1 &, IntegerQ[#^(1/3)] &], {n, 105}] (* Michael De Vlieger, Jul 28 2017 *)

PROG

(PARI) a(n) = sumdiv(n, d, ispower(d, 3)); \\ Michel Marcus, Jan 31 2015

CROSSREFS

Cf. A000005, A000578, A046951, A053150.

Sequence in context: A320267 A304327 A307428 * A325837 A050361 A072911

Adjacent sequences:  A061701 A061702 A061703 * A061705 A061706 A061707

KEYWORD

nonn,mult

AUTHOR

Henry Bottomley, Jun 18 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 00:52 EDT 2019. Contains 328315 sequences. (Running on oeis4.)