A093456 Product of composite numbers among next n numbers.

1, 1, 24, 720, 2520, 120960, 259459200, 1357171200, 4929724800, 42608389824000, 11912739135897600, 59907396092544000, 20458385028297216000, 7926428532945162240000, 4693751193479184764928000, 328774885640356760904499200000, 12797917159224592605450240000

Offset: 1

Author

Amarnath Murthy, Apr 03 2004

Keywords

• nonn
• less

Comments

Conjecture: There are finitely many numbers such that a(n) is not == 0 (mod a(n-1)). (Also mentioned in A093455.)

Product of all composite numbers between n*(n-1)/2+1 and n*(n+1)/2 (including boundaries). - Stefan Steinerberger, Apr 02 2006

Examples

			Sequence begins:
   1:             a(1) = 1.
   2  3:          a(2) = 1.
   4  5  6:       a(3) = 4*6 = 24.
   7  8  9 10:    a(4) = 8*9*10 = 720.
  11 12 13 14 15: a(5) = 12*14*15 = 2520.
  ...
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..244

Crossrefs

Cf. A000217, A057003, A093455, A093457.

Programs

Mathematica

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 *)
Module[{nn=20},Times@@Select[#,CompositeQ]&/@TakeList[Range[(nn(nn+1))/2],Range[nn]]] (* Harvey P. Dale, Dec 30 2024 *)

Formula

a(n) = A057003(n)/A093457(n). - Michel Marcus, Jan 14 2025

Extensions

More terms from Stefan Steinerberger, Apr 02 2006