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

3600, 7200, 10800, 14400, 18000, 21600, 25200, 28800, 32400, 36000, 39600, 43200, 46800, 50400, 54000, 57600, 61200, 64800, 68400, 72000, 75600, 79200, 82800, 86400, 90000, 93600, 97200, 100800, 104400, 108000, 111600, 115200, 118800, 122400, 126000, 129600, 133200

Offset: 1

Author

Reinhard Zumkeller, Aug 13 2004

Keywords

• nonn
• easy

Comments

a(n) = m * (A046083(k)*A046084(k)*A009000(k))^2 for appropriate, not necessarily unique m and k.

Examples

			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.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Tanya Khovanova, Recursive Sequences.
• Eric Weisstein's World of Mathematics, Pythagorean Triple.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. Pythagorean triples: A046083, A046084, A009000.

Cf. A044102, A094519, A169823.

Programs

Mathematica

Range[50]*3600 (* Paolo Xausa, Jul 01 2025 *)

PARI

my(x='x+O('x^38)); Vec(3600*x/(1-x)^2) \\ Elmo R. Oliveira, Jun 30 2025

Formula

a(n) = n*60^2.

From Elmo R. Oliveira, Jun 30 2025: (Start)

G.f.: 3600*x/(1-x)^2.

E.g.f.: 3600*x*exp(x).

a(n) = 60*A169823(n) = 100*A044102(n).

a(n) = 2*a(n-1) - a(n-2) for n > 2. (End)

Extensions

Name clarified by Tanya Khovanova, Jul 05 2021

More terms from Elmo R. Oliveira, Jun 30 2025