login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A093456
Product of composite numbers among next n numbers.
2
1, 1, 24, 720, 2520, 120960, 259459200, 1357171200, 4929724800, 42608389824000, 11912739135897600, 59907396092544000, 20458385028297216000, 7926428532945162240000, 4693751193479184764928000, 328774885640356760904499200000, 12797917159224592605450240000
OFFSET
1,3
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
LINKS
EXAMPLE
a(5) = 12*14*15 = 2520.
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 *)
CROSSREFS
Cf. A093455.
Sequence in context: A322746 A367330 A184274 * A189412 A246192 A246612
KEYWORD
nonn,less,changed
AUTHOR
Amarnath Murthy, Apr 03 2004
EXTENSIONS
More terms from Stefan Steinerberger, Apr 02 2006
STATUS
approved