A051539 - OEIS

%I #34 Oct 27 2023 22:00:44

%S 1,5,45,585,9945,69615,348075,10094175,111035925,4108329225,

%T 168441498225,168441498225,1179090487575,62491795841475,

%U 1187344120988025,72427991380269525,72427991380269525,1665843801746199075,121606597527472532475,121606597527472532475

%N a(n) is the least common multiple of {1, 5, 9, 13, 17, ..., 4n+1} (A016813).

%C This sequence coincides with sequence A097328 of denominators of 1 + 1/5 + 1/9 + 1/13 + ... + 1/(4n+1) iff n < 12. - _T. D. Noe_, Aug 04 2004

%H Harvey P. Dale, <a href="/A051539/b051539.txt">Table of n, a(n) for n = 0..866</a> (* First 201 terms from T. D. Noe *)

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

%e a(3) = LCM {1, 5, 9, 13} = 585.

%t Table[ Apply[ LCM, Join[{1}, Table[1 + 4i, {i, 0, n}]]], {n, 0, 19}]

%t nn=20;Table[LCM@@Take[4Range[0,nn-1]+1,n],{n,nn}] (* _Harvey P. Dale_, Jul 04 2011 *)

%t Table[LCM@@NestList[#+4&,1,n],{n,0,20}] (* _Harvey P. Dale_, Nov 21 2016 *)

%o (Magma) k:=77; [Lcm([h: h in [1..j by 4]]): j in [1..k by 4]];  // _Bruno Berselli_, May 03 2011

%o (PARI) a(n)=lcm(vector(n,i,4*n+1)) \\ _Charles R Greathouse IV_, Feb 09 2017

%Y Cf. A016813, A075136, A074598, A097329.

%K easy,nice,nonn

%O 0,2

%A _Asher Auel_

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

%E a(16) corrected by _T. D. Noe_, Feb 08 2008