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A368901 The least common multiple of the first n terms of Doudna sequence, A005940.

%I A368901 #12 Jun 24 2025 12:06:51
%S A368901 1,1,2,6,12,60,60,180,360,2520,2520,2520,2520,12600,12600,37800,75600,
%T A368901 831600,831600,831600,831600,831600,831600,831600,831600,5821200,
%U A368901 5821200,5821200,5821200,29106000,29106000,87318000,174636000,2270268000,2270268000,2270268000,2270268000,2270268000,2270268000,2270268000,2270268000
%N A368901 The least common multiple of the first n terms of Doudna sequence, A005940.
%H A368901 Michael De Vlieger, <a href="/A368901/b368901.txt">Table of n, a(n) for n = 0..16384</a>
%F A368901 a(0) = 1, and for n > 0, a(n) = lcm(A005940(n), a(n-1)).
%F A368901 a(0) = 1, and for n > 0, a(n) = A368900(n) * a(n-1).
%t A368901 Array[Set[a[#], #] &, 2]; m = 2; {1, 1, 2}~Join~Reap[Do[If[EvenQ[n], Set[a[n], 2 a[n/2]], Set[a[n], Times @@ Power @@@ Map[{Prime[PrimePi[#1] + 1], #2} & @@ # &, FactorInteger[a[(n + 1)/2] ] ] ] ]; Sow[m = LCM[m, a[n]]], {n, 3, 40}] ][[-1, 1]] (* _Michael De Vlieger_, Jun 24 2025 *)
%o A368901 (PARI)
%o A368901 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t) };
%o A368901 A368901(n) = lcm(vector(n,i,A005940(i)));
%Y A368901 Cf. A005940, A368900.
%Y A368901 Cf. also A003418.
%K A368901 nonn
%O A368901 0,3
%A A368901 _Antti Karttunen_ and _David James Sycamore_, Jan 10 2024