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
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).
Crossrefs
Cf. A061039.
Programs
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Haskell
import Data.Ratio ((%), denominator) a061040 n = denominator $ 1%9 - 1%n^2 -- Reinhard Zumkeller, Jan 03 2012
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Mathematica
Denominator[1/9-1/Range[3,50]^2] (* Harvey P. Dale, Jan 16 2012 *)
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PARI
a(n)=denominator(1/9 - 1/n^2) \\ Charles R Greathouse IV, Feb 07 2017
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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
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Sage
[denominator(1/9 -1/n^2) for n in (3..50)] # G. C. Greubel, Mar 10 2022
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
Comments