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A093456 Product of composite numbers among next n numbers. 2

%I

%S 1,1,24,720,2520,120960,259459200,1357171200,4929724800,

%T 42608389824000,11912739135897600,59907396092544000,

%U 20458385028297216000,7926428532945162240000,4693751193479184764928000,328774885640356760904499200000,12797917159224592605450240000

%N Product of composite numbers among next n numbers.

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

%C Product of all composite numbers between n*(n-1)/2+1 and n*(n+1)/2 (including boundaries). - _Stefan Steinerberger_, Apr 02 2006

%e a(5) = 12*14*15 = 2520.

%t 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 *)

%Y Cf. A093455.

%K nonn,less

%O 1,3

%A _Amarnath Murthy_, Apr 03 2004

%E More terms from _Stefan Steinerberger_, Apr 02 2006

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Last modified December 3 22:32 EST 2021. Contains 349468 sequences. (Running on oeis4.)