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A048785 a(0) = 0; a(n) = tau(n^3), where tau = number of divisors (A000005). 13
0, 1, 4, 4, 7, 4, 16, 4, 10, 7, 16, 4, 28, 4, 16, 16, 13, 4, 28, 4, 28, 16, 16, 4, 40, 7, 16, 10, 28, 4, 64, 4, 16, 16, 16, 16, 49, 4, 16, 16, 40, 4, 64, 4, 28, 28, 16, 4, 52, 7, 28, 16, 28, 4, 40, 16, 40, 16, 16, 4, 112, 4, 16, 28, 19, 16, 64, 4, 28, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The inverse Mobius transform of A074816. - R. J. Mathar, Feb 09 2011

a(n) is also the number of ordered triples (i,j,k) of positive integers such that i|n, j|n, k|n and i,j,k are pairwise relatively prime. - Geoffrey Critzer, Jan 11 2015

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = Sum_{d|n} 3^omega(d), where omega(x) is the number of distinct prime factors in the factorization of x. - Benoit Cloitre, Apr 14 2002

Multiplicative with a(p^e) = 3e+1. - Mitch Harris Jun 09 2005

L.g.f.: -log(Product_{k>=1} (1 - x^k)^(3^omega(k)/k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 26 2018

EXAMPLE

a(6) = 16 because there are 16 divisors of 6^3 = 216: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216.

Also there are 16 ordered triples of divisors of 6 that are pairwise relatively prime: (1,1,1), (1,1,2), (1,1,3), (1,1,6), (1, 2, 1), (1,2,3), (1,3,1), (1,3,2), (1,6,1), (2,1,1), (2,1,3), (2,3,1), (3,1,1), (3,1,2),(3,2,1), (6,1,1).

MAPLE

seq(numtheory:-tau(n^3), n=0..100); # Robert Israel, Jan 11 2015

MATHEMATICA

Join[{1}, Table[Product[3 k + 1, {k, FactorInteger[n][[All, 2]]}], {n, 2, 69}]] (* Geoffrey Critzer, Jan 11 2015 *)

Join[{0}, DivisorSigma[0, Range[70]^3]] (* Harvey P. Dale, Jan 23 2016 *)

PROG

(PARI) A048785(n) = if(!n, n, numdiv(n^3)); \\ Antti Karttunen, May 19 2017

CROSSREFS

Cf. A000005, A001221, A048691, A074816, A144943.

Sequence in context: A163106 A258972 A146564 * A271781 A243454 A204008

Adjacent sequences:  A048782 A048783 A048784 * A048786 A048787 A048788

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 18 01:36 EST 2019. Contains 319260 sequences. (Running on oeis4.)