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A110904 Integers that can be expressed as a product of triangular numbers in 3 different ways.

%I A110904 #11 Nov 29 2015 21:30:05
%S A110904 630,3780,14850,16380,21420,114660,131670,159390,178200,234360,401940,
%T A110904 478800,523260,556920,582120,712530,749700,835380,1455300,1753290,
%U A110904 1936935,2086920,2162160,2633400,2841300,3828825,4791150,5821200,6056820,6380010,6396390,6486480
%N A110904 Integers that can be expressed as a product of triangular numbers in 3 different ways.
%H A110904 Chai Wah Wu, <a href="/A110904/b110904.txt">Table of n, a(n) for n = 1..1007</a>
%e A110904 835380 = 91*9180 = 153*5460 = 630*1326.
%o A110904 (Python)
%o A110904 from __future__ import division
%o A110904 mmax = 10**3
%o A110904 tmax, A110904_dict = mmax*(mmax+1)//2, {}
%o A110904 ti = 0
%o A110904 for i in range(1,mmax+1):
%o A110904     ti += i
%o A110904     p = ti*i*(i-1)//2
%o A110904     for j in range(i,mmax+1):
%o A110904         p += ti*j
%o A110904         if p <= tmax:
%o A110904             A110904_dict[p] = A110904_dict[p]+1 if p in A110904_dict else 1
%o A110904         else:
%o A110904             break
%o A110904 A110904_list = sorted([i for i in A110904_dict if A110904_dict[i] == 3]) # _Chai Wah Wu_, Nov 29 2015
%Y A110904 Subsequence of A264961 and of A085780.
%K A110904 nonn
%O A110904 1,1
%A A110904 Luke T Pebody (ltp1000(AT)cam.ac.uk), Sep 21 2005
%E A110904 a(19)-a(20) from _R. J. Mathar_, Nov 29 2015