A109053 a(n) = lcm(n,12).
0, 12, 12, 12, 12, 60, 12, 84, 24, 36, 60, 132, 12, 156, 84, 60, 48, 204, 36, 228, 60, 84, 132, 276, 24, 300, 156, 108, 84, 348, 60, 372, 96, 132, 204, 420, 36, 444, 228, 156, 120, 492, 84, 516, 132, 180, 276, 564, 48, 588, 300, 204, 156, 636, 108, 660, 168
Offset: 0
Links
- Muniru A Asiru, Table of n, a(n) for n = 0..5000
- Index entries for linear recurrences with constant coefficients, 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).
- Index entries for sequences related to lcm's.
Programs
-
GAP
List([0..60],n->Lcm(n,12)); # Muniru A Asiru, Mar 04 2019
-
Magma
[LCM(n, 12): n in [0..60]]; // G. C. Greubel, Mar 06 2019
-
Mathematica
Array[LCM[#,12]&,60,0] (* Harvey P. Dale, Mar 26 2015 *)
-
PARI
concat(0, Vec(12*x*(1 + x + x^2 + x^3 + 5*x^4 + x^5 + 7*x^6 + 2*x^7 + 3*x^8 + 5*x^9 + 11*x^10 + x^11 + 11*x^12 + 5*x^13 + 3*x^14 + 2*x^15 + 7*x^16 + x^17 + 5*x^18 + x^19 + x^20 + x^21 + x^22) / (1 - 2*x^12 + x^24) + O(x^40))) \\ Colin Barker, Mar 04 2019
-
PARI
for(n=0,60, print1(lcm(n,12), ", ")) \\ G. C. Greubel, Mar 06 2019
-
Sage
[lcm(n,12) for n in range(0,57)] # Zerinvary Lajos, Jun 09 2009
Formula
a(n) = n*12/gcd(n, 12).
a(n) = 12*A051724(n). - R. J. Mathar, Feb 12 2019
From Colin Barker, Mar 04 2019: (Start)
G.f.: 12*x*(1 + x + x^2 + x^3 + 5*x^4 + x^5 + 7*x^6 + 2*x^7 + 3*x^8 + 5*x^9 + 11*x^10 + x^11 + 11*x^12 + 5*x^13 + 3*x^14 + 2*x^15 + 7*x^16 + x^17 + 5*x^18 + x^19 + x^20 + x^21 + x^22) / (1 - 2*x^12 + x^24).
a(n) = 2*a(n-12) - a(n-24) for n>23.
(End)
Sum_{k=1..n} a(k) ~ (77/24) * n^2. - Amiram Eldar, Nov 26 2022