A061040 Denominator of 1/9 - 1/n^2.

1, 144, 225, 12, 441, 576, 81, 900, 1089, 48, 1521, 1764, 75, 2304, 2601, 324, 3249, 3600, 147, 4356, 4761, 64, 5625, 6084, 729, 7056, 7569, 100, 8649, 9216, 363, 10404, 11025, 1296, 12321, 12996, 507, 14400, 15129, 588, 16641, 17424

Offset

3,2

Comments

See A061039 (numerators) for comments, references and links.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 3..1000

Friedrich Paschen, Zur Kenntnis ultraroter Linienspektra, Annalen der Physik 27, pp. 537-570 (1908).

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Formula

a(n) = denominator(n^2 - 9)/(9*n^2), n >= 3.

a(n) = (n^2)/9 if n == 3 or 24 (mod 27), a(n) = (n^2)/3 if n == 6 or 12 or 15 or 21 (mod 27), a(n) = n^2 if n == 0 (mod 9) and 9*n^2 otherwise. From the period length 27 sequence gcd(n^2 - 9, 9*n^2). - Wolfdieter Lang, Mar 15 2018

Mathematica

Denominator[1/9-1/Range[3, 50]^2] (* Harvey P. Dale, Jan 16 2012 *)

Prog

(Haskell)
import Data.Ratio ((%), denominator)
a061040 n = denominator $ 1%9 - 1%n^2 -- Reinhard Zumkeller, Jan 03 2012
(PARI) a(n)=denominator(1/9 - 1/n^2) \\ Charles R Greathouse IV, Feb 07 2017
(Python)
from math import gcd
def A061040(n): return 9*n**2//gcd(n**2-9, 9*n**2) # Chai Wah Wu, Apr 02 2021
(Sage) [denominator(1/9 -1/n^2) for n in (3..50)] # G. C. Greubel, Mar 10 2022

Crossrefs

Cf. A061039.

Sequence in context: A349064 A124144 A276564 * A159456 A316483 A064563

Adjacent sequences: A061037 A061038 A061039 * A061041 A061042 A061043

Keyword

nonn,frac,nice,easy

Author

N. J. A. Sloane, May 26 2001

Status

approved