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%I #13 Mar 13 2023 12:33:02
%S 0,36,900,1225,7056,32400,41616,44100,88209,108900,298116,705600,
%T 1368900,1413721,1498176,2924100,5336100,8643600,8820900,9217296,
%U 10432900,15210000,24147396,37088100,48024900,50893956,50979600,52490025,55353600,80568576
%N Perfect squares that are a product of two distinct triangular numbers.
%C a(47) = 1728896400 is the product of two distinct triangular numbers in two different ways. 1728896400 = A000217(8) * A000217(9800) = A000217(27) * A000217(3024). - _Donovan Johnson_, Sep 01 2012
%H Donovan Johnson, <a href="/A169836/b169836.txt">Table of n, a(n) for n = 1..1000</a>
%H Erich Friedman, <a href="https://erich-friedman.github.io/numbers.html">What's Special About This Number?</a> (See entry 7056.)
%F a(n) = (A175497(n))^2. [From _R. J. Mathar_, Jun 03 2010]
%e Examples: 900=3*300. 7056 = 6*1176. 1368900 = 6*228150. 44100 = 36*1225.
%o (PARI) istriangular(n)=issquare(8*n+1)
%o isok(n) = {if (issquare(n), d = divisors(n); fordiv(n, d, if (d > sqrtint(n), break); if ((d != n/d) && istriangular(d) && istriangular(n/d), return (1)););); return (0);} \\ _Michel Marcus_, Jul 24 2013
%o (Python)
%o from itertools import count, islice, takewhile
%o from sympy import divisors
%o from sympy.ntheory.primetest import is_square
%o def A169836_gen(): # generator of terms
%o return filter(lambda k:not k or any(map(lambda d: is_square((d<<3)+1) and is_square((k//d<<3)+1), takewhile(lambda d:d**2<k,divisors(k)))),(m**2 for m in count(0)))
%o A169836_list = list(islice(A169836_gen(),20)) # _Chai Wah Wu_, Mar 13 2023
%Y Cf. A000217, A054731, A169835.
%K nonn
%O 1,2
%A R. J. Mathar, May 30 2010
%E More terms from _R. J. Mathar_, Jun 03 2010
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