cp's OEIS Frontend

A070292 a(n) = lcm(12,n)/gcd(12,n).

%I A070292 #23 Oct 07 2023 05:06:20
%S A070292 12,6,4,3,60,2,84,6,12,30,132,1,156,42,20,12,204,6,228,15,28,66,276,2,
%T A070292 300,78,36,21,348,10,372,24,44,102,420,3,444,114,52,30,492,14,516,33,
%U A070292 60,138,564,4,588,150,68,39,636,18,660,42,76,174,708,5,732,186,84,48
%N A070292 a(n) = lcm(12,n)/gcd(12,n).
%H A070292 Colin Barker, <a href="/A070292/b070292.txt">Table of n, a(n) for n = 1..1000</a>
%H A070292 <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,-1).
%F A070292 a(n) = A109053(n)/A109015(n) = 12*n/A109015(n)^2. - _R. J. Mathar_, Feb 12 2019
%F A070292 a(n) = 2*a(n-12) - a(n-24). - _R. J. Mathar_, Feb 12 2019
%F A070292 G.f.: x*(12 + 6*x + 4*x^2 + 3*x^3 + 60*x^4 + 2*x^5 + 84*x^6 + 6*x^7 + 12*x^8 + 30*x^9 + 132*x^10 + x^11 + 132*x^12 + 30*x^13 + 12*x^14 + 6*x^15 + 84*x^16 + 2*x^17 + 60*x^18 + 3*x^19 + 4*x^20 + 6*x^21 + 12*x^22) / (x^24 - 2*x^12 + 1). - _Colin Barker_, Mar 05 2019
%F A070292 Sum_{k=1..n} a(k) ~ (703/288)*n^2. - _Amiram Eldar_, Oct 07 2023
%o A070292 (PARI) for(n=1,100,print1(lcm(12,n)/gcd(n,12),","))
%o A070292 (PARI) Vec(x*(12 + 6*x + 4*x^2 + 3*x^3 + 60*x^4 + 2*x^5 + 84*x^6 + 6*x^7 + 12*x^8 + 30*x^9 + 132*x^10 + x^11 + 132*x^12 + 30*x^13 + 12*x^14 + 6*x^15 + 84*x^16 + 2*x^17 + 60*x^18 + 3*x^19 + 4*x^20 + 6*x^21 + 12*x^22) / (x^24 - 2*x^12 + 1) + O(x^60)) \\ _Colin Barker_, Mar 05 2019
%o A070292 (Python)
%o A070292 from math import gcd, lcm
%o A070292 def a(n): return lcm(12, n)//gcd(12, n)
%o A070292 print([a(n) for n in range(1, 65)]) # _Michael S. Branicky_, Dec 06 2021
%Y A070292 Cf. A070290, A070291, A070293, A109015, A109053.
%K A070292 easy,nonn
%O A070292 1,1
%A A070292 _Amarnath Murthy_, May 10 2002
%E A070292 More terms from _Benoit Cloitre_, May 16 2002