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A060462 n! is divisible by n*(n+1)/2. 17

%I

%S 1,3,5,7,8,9,11,13,14,15,17,19,20,21,23,24,25,26,27,29,31,32,33,34,35,

%T 37,38,39,41,43,44,45,47,48,49,50,51,53,54,55,56,57,59,61,62,63,64,65,

%U 67,68,69,71,73,74,75,76,77,79,80,81,83,84,85,86,87,89,90,91,92,93,94

%N n! is divisible by n*(n+1)/2.

%C n! / (n-th triangular number) is an integer.

%C a(k) = A072668(k) for k>0.

%D J. D. E. Konhauser et al., Which Way Did The Bicycle Go?, Problem 98, pp. 29; 145-146, MAA Washington DC, 1996.

%H Harry J. Smith, <a href="/A060462/b060462.txt">Table of n, a(n) for n = 0..2000</a>

%e 5*4*3*2*1=120 is divisible by 5 + 4 + 3 + 2 + 1 = 15.

%p for n from 1 to 300 do if n! mod (n*(n+1)/2) = 0 then printf(`%d,`,n) fi:od:

%t Select[Range[94], Mod[#!, #*(# + 1)/2] == 0 &] (* _Jayanta Basu_, Apr 24 2013 *)

%o (PARI) { f=1; t=0; n=-1; for (m=1, 4000, f*=m; t+=m; if (f%t==0, write("b060462.txt", n++, " ", m)); if (n==2000, break); ) } \\ _Harry J. Smith_, Jul 05 2009

%K nonn

%O 0,2

%A _Michel ten Voorde_ Apr 09 2001

%E Corrected and extended by _Henry Bottomley_ and _James A. Sellers_, Apr 11 2001

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)