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

1, 1, 2, 6, 12, 60, 60, 180, 360, 2520, 2520, 2520, 2520, 12600, 12600, 37800, 75600, 831600, 831600, 831600, 831600, 831600, 831600, 831600, 831600, 5821200, 5821200, 5821200, 5821200, 29106000, 29106000, 87318000, 174636000, 2270268000, 2270268000, 2270268000, 2270268000, 2270268000, 2270268000, 2270268000, 2270268000

Offset: 0

Author

Antti Karttunen and David James Sycamore, Jan 10 2024

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A005940, A368900.

Cf. also A003418.

Programs

Mathematica

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 *)

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t) };
A368901(n) = lcm(vector(n,i,A005940(i)));

Formula

a(0) = 1, and for n > 0, a(n) = lcm(A005940(n), a(n-1)).

a(0) = 1, and for n > 0, a(n) = A368900(n) * a(n-1).