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 A093456 #24 Jan 14 2025 06:04:11
%S A093456 1,1,24,720,2520,120960,259459200,1357171200,4929724800,
%T A093456 42608389824000,11912739135897600,59907396092544000,
%U A093456 20458385028297216000,7926428532945162240000,4693751193479184764928000,328774885640356760904499200000,12797917159224592605450240000
%N A093456 Product of composite numbers among next n numbers.
%C A093456 Conjecture: There are finitely many numbers such that a(n) is not == 0 (mod a(n-1)). (Also mentioned in A093455.)
%C A093456 Product of all composite numbers between n*(n-1)/2+1 and n*(n+1)/2 (including boundaries). - _Stefan Steinerberger_, Apr 02 2006
%H A093456 Harvey P. Dale, <a href="/A093456/b093456.txt">Table of n, a(n) for n = 1..244</a>
%F A093456 a(n) = A057003(n)/A093457(n). - _Michel Marcus_, Jan 14 2025
%e A093456 Sequence begins:
%e A093456 1: a(1) = 1.
%e A093456 2 3: a(2) = 1.
%e A093456 4 5 6: a(3) = 4*6 = 24.
%e A093456 7 8 9 10: a(4) = 8*9*10 = 720.
%e A093456 11 12 13 14 15: a(5) = 12*14*15 = 2520.
%e A093456 ...
%t A093456 Table[a := Range[n*(n - 1)/2 + 1, n*(n + 1)/2]; b := Select[a, Not[PrimeQ[ # ]] &]; Product[b[[i]], {i, 1, Length[b]}], {n, 1, 20}] (* _Stefan Steinerberger_, Apr 02 2006 *)
%t A093456 Module[{nn=20},Times@@Select[#,CompositeQ]&/@TakeList[Range[(nn(nn+1))/2],Range[nn]]] (* _Harvey P. Dale_, Dec 30 2024 *)
%Y A093456 Cf. A000217, A057003, A093455, A093457.
%K A093456 nonn,less
%O A093456 1,3
%A A093456 _Amarnath Murthy_, Apr 03 2004
%E A093456 More terms from _Stefan Steinerberger_, Apr 02 2006