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

1,2

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

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A000578 (cubes).

Sequence in context: A205704 A337212 A093023 * A246639 A287922 A321483

Adjacent sequences: A057094 A057095 A057096 * A057098 A057099 A057100

Keyword

nonn

Author

Henry Bottomley, Aug 01 2000

Status

approved