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

1,1

Comments

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

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).

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)

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. Pythagorean triples: A046083, A046084, A009000.

Cf. A044102, A094519, A169823.

Sequence in context: A391091 A391085 A391086 * A306492 A364990 A250439

Adjacent sequences: A096469 A096470 A096471 * A096473 A096474 A096475

Keyword

nonn,easy

Author

Reinhard Zumkeller, Aug 13 2004

Extensions

Name clarified by Tanya Khovanova, Jul 05 2021

More terms from Elmo R. Oliveira, Jun 30 2025

Status

approved