A051536 a(n) = least common multiple of {1, 4, 7, 10, 13 ..., 3n+1} (A016777).

1, 4, 28, 140, 1820, 7280, 138320, 1521520, 7607600, 7607600, 235835600, 4009205200, 148340592400, 148340592400, 6378645473200, 146708845883600, 1026961921185200, 1026961921185200, 1026961921185200, 29781895714370800

Offset: 0

Author

Asher Auel

Keywords

• easy
• frac
• nice
• nonn

Comments

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

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

Examples

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

Links

• T. D. Noe, Table of n, a(n) for n = 0..200
• Index entries for sequences related to lcm's

Crossrefs

Cf. A016777.

The numerators are in A074596.

Cf. A075135, A059457, A051540.

Programs

Haskell

a051536 n = a051536_list !! (n-1)
a051536_list = scanl1 lcm a016777_list
-- Reinhard Zumkeller, Feb 28 2013, Feb 10 2012

Magma

k:=58; [Lcm([h: h in [1..j by 3]]): j in [1..k by 3]]; // Bruno Berselli, May 03 2011

Mathematica

Table[ Denominator[ Sum[1/i, {i, 1/3, n}]], {n, 1, 20}]
Table[ Apply[ LCM, Join[{1}, Table[1 + 3i, {i, 0, n}]]], {n, 0, 19}]
Table[Denominator[Total[1/Range[1, 3n+1, 3]]], {n, 0, 29}]
Module[{nn=30,lst},lst=3*Range[0,nn]+1;Table[LCM@@Take[lst,n],{n,nn}]] (* Harvey P. Dale, Sep 30 2012 *)

PARI

a(n)=lcm(vector(n,i,3*i+1)) \\ Charles R Greathouse IV, Feb 09 2017

Extensions

Edited by Robert G. Wilson v, Aug 27 2002