cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A057097 #20 Jan 27 2020 03:33:55
%S A057097 1,8,13,27,34,64,70,104,125,203,216,246,259,272,343,351,512,560,671,
%T A057097 729,832,918,1000,1092,1113,1331,1547,1624,1625,1728,1890,1968,2002,
%U A057097 2072,2176,2197,2744,2808,3164,3212,3333,3375,3927,4096,4250,4459,4480
%N A057097 Products of the three sides of Pythagorean triangles divided by 60.
%C A057097 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).
%C A057097 By considering the Pythagorean triangle (3k, 4k, 5k) we see that all numbers k^3 are in the sequence. - _Sergey Pavlov_, Mar 29 2017
%H A057097 Vincenzo Librandi, <a href="/A057097/b057097.txt">Table of n, a(n) for n = 1..386</a>
%F A057097 a(n) = A057096(n)/60 = A057098(n)*A057099(n)*A057100(n)/60.
%e A057097 a(1) = 3*4*5/60 = 1.
%t A057097 (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 *)
%Y A057097 Cf. A000578 (cubes).
%K A057097 nonn
%O A057097 1,2
%A A057097 _Henry Bottomley_, Aug 01 2000