cp's OEIS Frontend

A189046 a(n) = lcm(n,n+1,n+2,n+3,n+4,n+5)/60.

%I A189046 #32 Apr 20 2023 14:40:09
%S A189046 0,1,7,14,42,42,462,462,858,3003,1001,4004,6188,18564,27132,3876,
%T A189046 27132,74613,100947,67298,17710,230230,296010,188370,237510,118755,
%U A189046 736281,453096,553784,1344904,324632
%N A189046 a(n) = lcm(n,n+1,n+2,n+3,n+4,n+5)/60.
%C A189046 a(n) mod 2 has a period of 8, repeating [0,1,1,0,0,0,0,0].
%H A189046 Nathaniel Johnston, <a href="/A189046/b189046.txt">Table of n, a(n) for n = 0..2000</a>
%H A189046 <a href="/index/Rec#order_105">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 7, 0, 0, 0, 0, -28, 0, 0, 0, 0, 84, 0, 0, 0, 0, -203, 0, 0, 0, 0, 413, 0, 0, 0, 0, -728, 0, 0, 0, 0, 1128, 0, 0, 0, 0, -1554, 0, 0, 0, 0, 1918, 0, 0, 0, 0, -2128, 0, 0, 0, 0, 2128, 0, 0, 0, 0, -1918, 0, 0, 0, 0, 1554, 0, 0, 0, 0, -1128, 0, 0, 0, 0, 728, 0, 0, 0, 0, -413, 0, 0, 0, 0, 203, 0, 0, 0, 0, -84, 0, 0, 0, 0, 28, 0, 0, 0, 0, -7, 0, 0, 0, 0, 1).
%H A189046 <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>.
%F A189046 a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(4*(n^4 mod 5)+1)/(1800*((n^3 mod 4)+((n-1)^3 mod 4)+1)).
%F A189046 a(n) = binomial(n+5,6)/(gcd(n,5)*(A021913(n-1)+1)).
%F A189046 a(n) = binomial(n+5,6)/(gcd(n,5)*floor(((n-1) mod 4)/2+1)). - _Gary Detlefs_, Apr 22 2011
%F A189046 Sum_{n>=1} 1/a(n) = 92 + (54/5-18*sqrt(5)+6*sqrt(178-398/sqrt(5)))*Pi. - _Amiram Eldar_, Sep 29 2022
%p A189046 seq(lcm(n,n+1,n+2,n+3,n+4,n+5)/60,n=0..30)
%t A189046 Table[(LCM@@(n+Range[0,5]))/60,{n,0,40}]  (* _Harvey P. Dale_, Apr 17 2011 *)
%o A189046 (PARI) a(n)=lcm([n..n+5])/60 \\ _Charles R Greathouse IV_, Sep 30 2016
%Y A189046 Cf. A000217 ( = lcm(n,n+1)/2), A021913, A067046, A067047, A067048.
%K A189046 nonn,easy
%O A189046 0,3
%A A189046 _Gary Detlefs_, Apr 15 2011