A051536 - OEIS

%I #47 Feb 20 2024 02:33:41

%S 1,4,28,140,1820,7280,138320,1521520,7607600,7607600,235835600,

%T 4009205200,148340592400,148340592400,6378645473200,146708845883600,

%U 1026961921185200,1026961921185200,1026961921185200,29781895714370800

%N a(n) = least common multiple of {1, 4, 7, 10, 13 ..., 3n+1} (A016777).

%C This sequence coincides with the sequence of denominators of 1 + 1/4 + 1/7 + 1/10 + ... + 1/(3*n + 1) for n < 29. - _T. D. Noe_, Aug 04 2004

%C The sequence coincides with the sequence of denominators of 1 - 1/4 + 1/7 - 1/10 + ... + (-1)^n/(3*n + 1) for n < 45. - _Peter Bala_, Feb 19 2024

%H T. D. Noe, <a href="/A051536/b051536.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>

%e a(4) = lcm of {1, 4, 7, 10, 13} = 1820.

%t Table[ Denominator[ Sum[1/i, {i, 1/3, n}]], {n, 1, 20}]

%t Table[ Apply[ LCM, Join[{1}, Table[1 + 3i, {i, 0, n}]]], {n, 0, 19}]

%t Table[Denominator[Total[1/Range[1, 3n+1, 3]]], {n, 0, 29}]

%t Module[{nn=30,lst},lst=3*Range[0,nn]+1;Table[LCM@@Take[lst,n],{n,nn}]] (* _Harvey P. Dale_, Sep 30 2012 *)

%o (Magma) k:=58; [Lcm([h: h in [1..j by 3]]): j in [1..k by 3]]; // _Bruno Berselli_, May 03 2011

%o (Haskell)

%o a051536 n = a051536_list !! (n-1)

%o a051536_list = scanl1 lcm a016777_list

%o -- Reinhard Zumkeller, Feb 28 2013, Feb 10 2012

%o (PARI) a(n)=lcm(vector(n,i,3*i+1)) \\ _Charles R Greathouse IV_, Feb 09 2017

%Y Cf. A016777.

%Y The numerators are in A074596.

%Y Cf. A075135, A059457, A051540.

%K easy,frac,nice,nonn

%O 0,2

%A _Asher Auel_

%E Edited by _Robert G. Wilson v_, Aug 27 2002