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A068084 Smallest triangular number which is a multiple (>1) of the n-th triangular number.

%I A068084 #13 Jan 19 2016 23:46:11
%S A068084 3,6,36,120,45,105,1176,2016,630,990,528,780,3003,210,3240,32640,9180,
%T A068084 11628,2850,630,3003,26565,16836,20100,44850,52650,17766,20706,10440,
%U A068084 12090,461280,61776,11781,3570,25200,43956,221445,30381,5460,189420
%N A068084 Smallest triangular number which is a multiple (>1) of the n-th triangular number.
%H A068084 Zak Seidov and Chai Wah Wu, <a href="/A068084/b068084.txt">Table of n, a(n) for n = 1..10000</a> n = 1..1000 from Zak Seidov
%e A068084 The fifth triangular number is 15; the next triangular number that's divisible by 15 is 45, so a(5)=45.
%t A068084 a[n_] := For[k=n+1, True, k++, If[Mod[k(k+1), n(n+1)]==0, Return[k(k+1)/2]]]
%o A068084 (Python)
%o A068084 from __future__ import division
%o A068084 def A068084(n):
%o A068084     u,v,t = 4*(n+1),(2*(n+1))**2-1,4*n*(n+1)
%o A068084     while True:
%o A068084         if not v % t:
%o A068084             return v//8
%o A068084         v += u+1
%o A068084         u += 2 # _Chai Wah Wu_, Jan 13 2016
%K A068084 easy,nonn
%O A068084 1,1
%A A068084 _Amarnath Murthy_, Feb 18 2002
%E A068084 Edited by _Dean Hickerson_, Feb 20 2002