login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A144615 a(n) = A000203(3n+2). 3
3, 6, 15, 12, 24, 18, 42, 24, 42, 30, 63, 48, 60, 42, 84, 48, 93, 54, 120, 60, 96, 84, 126, 72, 114, 96, 186, 84, 132, 90, 168, 120, 171, 102, 210, 108, 216, 114, 210, 144, 186, 156, 255, 132, 204, 138, 336, 168, 222, 150, 300, 192, 240, 192, 294, 168, 324, 174, 372, 180, 336 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).

LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..10000

FORMULA

Expansion of q^(-2/3) * c(q)^2 / 3 in powers of q where c() is a cubic AGM theta function. - Michael Somos, Jun 07 2012

Expansion of q^(-2/3) * 3 * (eta(q^3)^3 / eta(q))^2 in powers of q. - Michael Somos, Jun 07 2012

a(n) = A000203(A016789(n)). - Michel Marcus, Jul 14 2015

a(n) = 3*A033686(n). - Robert G. Wilson v, Jan 12 2018

EXAMPLE

G.f. = 3 + 6*x + 15*x^2 + 12*x^3 + 24*x^4 + 18*x^5 + 42*x^6 + 24*x^7 + 42*x^8 + ...

G.f. = 3*q^2 + 6*q^5 + 15*q^8 + 12*q^11 + 24*q^14 + 18*q^17 + 42*q^20 + 24*q^23 + ...

MAPLE

with(numtheory):

seq(sigma(3*n+2), n=0..10^3); # Muniru A Asiru, Dec 29 2017

MATHEMATICA

a[ n_] := If[ n < 0, 0, DivisorSigma[ 1, 3 n + 2]]; (* Michael Somos, Jul 14 2015 *)

a[ n_] := SeriesCoefficient[ 3 (QPochhammer[ x^3]^3 / QPochhammer[ x])^2, {x, 0, n}]; (* Michael Somos, Jul 14 2015 *)

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( 3 * (eta(x^3 + A)^3 / eta(x + A))^2, n))}; /* Michael Somos, Jun 07 2012 */

(PARI) a(n)=sigma(3*n+2); \\ Michel Marcus, Jul 14 2015

(GAP) sequence := List([0..10^4], n->Sigma(3*n+2)); # Muniru A Asiru, Dec 29 2017

(Magma) [SumOfDivisors(3*n+2): n in [0..70]]; // Vincenzo Librandi, Jan 19 2018

CROSSREFS

Cf. A000203, A016789, A033686.

Sequence in context: A066107 A162276 A261955 * A088698 A105802 A285844

Adjacent sequences: A144612 A144613 A144614 * A144616 A144617 A144618

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 15 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 November 28 17:22 EST 2022. Contains 358421 sequences. (Running on oeis4.)