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A061704 Number of cubes dividing n. 18
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

LINKS

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

Index entries for sequences computed from exponents in factorization of n

FORMULA

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

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 *)

f[p_, e_] := 1 + Floor[e/3]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 15 2020 *)

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

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Last modified October 20 12:27 EDT 2020. Contains 337904 sequences. (Running on oeis4.)