This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A171645 #8 Oct 02 2024 19:21:35
%S A171645 2,4,8,12,18,30,50,70,98,154,242,286,338,442,578,646,722,874,1058,
%T A171645 1334,1682,1798,1922,2294,2738
%N A171645 Partial products of Product_{n=1..inf.} (p(n)/p(n-1)*p(n)/p(n-1)), = 2*2*2*(3/2)*(3/2)*(5/3)*(5/3)*(7/5)*(7/5)*(11/7)*(11/7)*...; p = primes, A000040, a(1) = 2.
%C A171645 Analogous formulas using A000041 terms = A171646; Fibonacci numbers, A006498; factorials, A010551.
%H A171645 Harvey P. Dale, <a href="/A171645/b171645.txt">Table of n, a(n) for n = 1..1000</a>
%F A171645 Partial products of Product_{n=1..inf.} (p(n)/p(n-1)*p(n)/p(n-1)), =
%F A171645 2*2*2*(3/2)*(3/2)*(5/3)*(5/3)*(7/5)*(7/5)*(11/7)*(11/7)*...; p = primes,
%F A171645 A000040, a(1) = 2.
%F A171645 a(n)=2*A057602(n-1). [From _R. J. Mathar_, Dec 15 2009]
%e A171645 a(10) = 154 = 2*2*2*(3/2)*(3/2)*(5/3)*(5/3)*(7/5)*(7/5)*(11/7).
%t A171645 FoldList[Times,Join[{2,2,2},Flatten[{#[[2]]/#[[1]],#[[2]]/#[[1]]}&/@Partition[Prime[Range[20]],2,1]]]] (* _Harvey P. Dale_, Oct 02 2024 *)
%Y A171645 Cf. A171646, A006498, A010551.
%K A171645 nonn
%O A171645 1,1
%A A171645 _Gary W. Adamson_, Dec 13 2009