A057097 Products of the three sides of Pythagorean triangles divided by 60.

1, 8, 13, 27, 34, 64, 70, 104, 125, 203, 216, 246, 259, 272, 343, 351, 512, 560, 671, 729, 832, 918, 1000, 1092, 1113, 1331, 1547, 1624, 1625, 1728, 1890, 1968, 2002, 2072, 2176, 2197, 2744, 2808, 3164, 3212, 3333, 3375, 3927, 4096, 4250, 4459, 4480

Offset: 1

Author

Henry Bottomley, Aug 01 2000

Keywords

• nonn

Comments

Note that if m appears in the sequence then k^3*m will also appear for all k and so in particular all cubes appear; the reverse is not always true (for example, 32*255*257/60 = 34952 = 2^3*4369 eventually appears, but 4369 does not).

By considering the Pythagorean triangle (3k, 4k, 5k) we see that all numbers k^3 are in the sequence. - Sergey Pavlov, Mar 29 2017

Examples

			a(1) = 3*4*5/60 = 1.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..386

Crossrefs

Cf. A000578 (cubes).

Programs

Mathematica

(k=600000; lst={}; Do[Do[If[IntegerQ[a=Sqrt[c^2 - b^2]], If[a>=b, Break[]]; x=a b c; If[x<=k, AppendTo[lst, x]]], {b, c - 1, 4, -1}], {c, 5, 400, 1}]; Union@lst)/60 (* Vincenzo Librandi Mar 30 2017 *)

Formula

a(n) = A057096(n)/60 = A057098(n)*A057099(n)*A057100(n)/60.