cp's OEIS Frontend

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

%I A061040 #41 Oct 09 2023 11:05:47
%S A061040 1,144,225,12,441,576,81,900,1089,48,1521,1764,75,2304,2601,324,3249,
%T A061040 3600,147,4356,4761,64,5625,6084,729,7056,7569,100,8649,9216,363,
%U A061040 10404,11025,1296,12321,12996,507,14400,15129,588,16641,17424
%N A061040 Denominator of 1/9 - 1/n^2.
%C A061040 See A061039 (numerators) for comments, references and links.
%H A061040 Reinhard Zumkeller, <a href="/A061040/b061040.txt">Table of n, a(n) for n = 3..1000</a>
%H A061040 Friedrich Paschen, <a href="https://doi.org/10.1002/andp.19083321303">Zur Kenntnis ultraroter Linienspektra</a>, Annalen der Physik 27, pp. 537-570 (1908).
%H A061040 <a href="/index/Rec#order_81">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A061040 a(n) = denominator(n^2 - 9)/(9*n^2), n >= 3.
%F A061040 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
%t A061040 Denominator[1/9-1/Range[3,50]^2] (* _Harvey P. Dale_, Jan 16 2012 *)
%o A061040 (Haskell)
%o A061040 import Data.Ratio ((%), denominator)
%o A061040 a061040 n = denominator $ 1%9 - 1%n^2 -- _Reinhard Zumkeller_, Jan 03 2012
%o A061040 (PARI) a(n)=denominator(1/9 - 1/n^2) \\ _Charles R Greathouse IV_, Feb 07 2017
%o A061040 (Python)
%o A061040 from math import gcd
%o A061040 def A061040(n): return 9*n**2//gcd(n**2-9,9*n**2) # _Chai Wah Wu_, Apr 02 2021
%o A061040 (Sage) [denominator(1/9 -1/n^2) for n in (3..50)] # _G. C. Greubel_, Mar 10 2022
%Y A061040 Cf. A061039.
%K A061040 nonn,frac,nice,easy
%O A061040 3,2
%A A061040 _N. J. A. Sloane_, May 26 2001