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 A077542 Least number of terms required in the product (k+1)(k+2)... to make it a multiple of the product of next n number, where k = n(n+1)/2. 2

%I #4 Dec 05 2013 19:55:53

%S 1,3,4,6,6,7,11,10,10,13,14,17,14,20,25,19,21,19,32,24,28,34,25,33,27,

%T 36,46,35,42,31,53,36,49,54,41,44,39,63,46,56,62,51,59,54,71,81,57,70,

%U 56,83,88,77,84,67,95,69,98,97,84,96,71,84,75,100,102,78,95,79,125

%N Least number of terms required in the product (k+1)(k+2)... to make it a multiple of the product of next n number, where k = n(n+1)/2.

%C For n > 5, a(n) >= 2p - n, where p is the largest prime less than n(n+1)/2.

%F Let A077540(n) = (k+1)(k+2)...(k+r) where k = n(n+1)/2 then a(n) = r.

%e a(3) = 4 as A077540(3) = 5040 = 7*8*9*10 = (6+1)(6+2)(6+3)(6+4).

%o (PARI) for(n=1,100,p=1:t=n*(n+1)/2:f=1:for(k=1,n,f=f*(n+k)):for(k=1,10^9,p=p*(t+k): if(p%f==0,print1(k","):break)))

%Y Cf. A077540, A077541.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Nov 09 2002

%E Corrected and extended by _Ralf Stephan_, Mar 27 2003

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Last modified August 7 08:03 EDT 2024. Contains 375008 sequences. (Running on oeis4.)