A078928 Smallest p for which there are exactly n primitive Pythagorean triangles with perimeter p; i.e., smallest p such that A070109(p) = n.

12, 1716, 14280, 317460, 1542684, 6240360, 19399380, 63303240, 239168580, 397687290, 458948490, 813632820, 562582020, 2824441620, 3346393050, 6915878970, 6469693230, 8720021310, 9146807670, 8254436190, 23065862820, 25859373540, 202536455550

Offset: 1

Author

Dean Hickerson, Dec 15 2002

Keywords

• nonn

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.

Least perimeter common to exactly n primitive Pythagorean triangles. - Lekraj Beedassy, May 14 2004

Examples

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

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)
• Shyam Sunder Gupta, Number Curiosities, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 23, 567-604.
• C. B. T. (Reviewer), Review of Andrew S. Anema, A table of primitive Pythagorean triangle with identical perimeters, Mathematical Tables and Other Aids to Computation, Vol. 10, No. 53 (Jan., 1956), pp. 35-36.

Crossrefs

a(n) = 2*A078927(n). Cf. A070109.

Programs

Mathematica

oddpart[n_] := If[OddQ[n], n, oddpart[n/2]]; ct[p_] := Length[Select[Divisors[oddpart[p/2]], p/2<#^2
				

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(39) from Peter T. C. Radden, Dec 29 2012