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).

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