cp's OEIS Frontend

A096472 Numbers containing squares of Pythagorean triples in their divisor set.

%I A096472 #27 Jul 05 2025 14:16:08
%S A096472 3600,7200,10800,14400,18000,21600,25200,28800,32400,36000,39600,
%T A096472 43200,46800,50400,54000,57600,61200,64800,68400,72000,75600,79200,
%U A096472 82800,86400,90000,93600,97200,100800,104400,108000,111600,115200,118800,122400,126000,129600,133200
%N A096472 Numbers containing squares of Pythagorean triples in their divisor set.
%C A096472 a(n) = m * (A046083(k)*A046084(k)*A009000(k))^2 for appropriate, not necessarily unique m and k.
%H A096472 Paolo Xausa, <a href="/A096472/b096472.txt">Table of n, a(n) for n = 1..10000</a>
%H A096472 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A096472 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>.
%H A096472 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A096472 a(n) = n*60^2.
%F A096472 From _Elmo R. Oliveira_, Jun 30 2025: (Start)
%F A096472 G.f.: 3600*x/(1-x)^2.
%F A096472 E.g.f.: 3600*x*exp(x).
%F A096472 a(n) = 60*A169823(n) = 100*A044102(n).
%F A096472 a(n) = 2*a(n-1) - a(n-2) for n > 2. (End)
%e A096472 5^2 + 12^2 = 13^2: 5^2, 12^2 and 13^2 are divisors of 608400 = (13*5*3*2^2)^2, therefore 608400 is a term.
%t A096472 Range[50]*3600 (* _Paolo Xausa_, Jul 01 2025 *)
%o A096472 (PARI) my(x='x+O('x^38)); Vec(3600*x/(1-x)^2) \\ _Elmo R. Oliveira_, Jun 30 2025
%Y A096472 Cf. Pythagorean triples: A046083, A046084, A009000.
%Y A096472 Cf. A044102, A094519, A169823.
%K A096472 nonn,easy
%O A096472 1,1
%A A096472 _Reinhard Zumkeller_, Aug 13 2004
%E A096472 Name clarified by _Tanya Khovanova_, Jul 05 2021
%E A096472 More terms from _Elmo R. Oliveira_, Jun 30 2025