A078927 Smallest s for which there are exactly n primitive Pythagorean triangles with perimeter 2s; i.e., smallest s such that A078926(s) = n.

6, 858, 7140, 158730, 771342, 3120180, 9699690, 31651620, 119584290, 198843645, 229474245, 406816410, 281291010, 1412220810, 1673196525, 3457939485, 3234846615, 4360010655, 4573403835, 4127218095, 11532931410, 12929686770, 101268227775

Offset

1,1

Comments

A Pythagorean triangle is a right triangle whose edge lengths are all integers; such a triangle is 'primitive' if the lengths are relatively prime.

Links

Derek J. C. Radden and Peter T. C. Radden, Table of n, a(n) for n=1..39 (terms 1 through 15 were computed by Derek J. C. Radden)

Example

a(2)=858; the primitive Pythagorean triangles with edge lengths (364, 627, 725) and (195, 748, 773) both have perimeter 2*858 = 1716.

Mathematica

oddpart[n_] := If[OddQ[n], n, oddpart[n/2]]; ct[p_] := Length[Select[Divisors[oddpart[p/2]], p/2<#^2<p&&GCD[ #, p/2/# ]==1&]]; a[n_] := For[s=1, True, s++, If[ct[2s]==n, Return[s]]]

Crossrefs

a(n) = A078928(n)/2. Cf. A078926.

Sequence in context: A378386 A281690 A201141 * A064430 A332186 A279304

Adjacent sequences: A078924 A078925 A078926 * A078928 A078929 A078930

Keyword

nonn

Author

Dean Hickerson, Dec 15 2002

Extensions

a(8) from Robert G. Wilson v, Dec 19 2002

a(9)-a(15) from Derek J C Radden, Dec 22 2012

a(16)-a(23) from Peter T. C. Radden, Dec 29 2012

Status

approved