A061040 - OEIS

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

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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