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

%I A078928 #34 Mar 10 2025 11:46:22
%S A078928 12,1716,14280,317460,1542684,6240360,19399380,63303240,239168580,
%T A078928 397687290,458948490,813632820,562582020,2824441620,3346393050,
%U A078928 6915878970,6469693230,8720021310,9146807670,8254436190,23065862820,25859373540,202536455550
%N A078928 Smallest p for which there are exactly n primitive Pythagorean triangles with perimeter p; i.e., smallest p such that A070109(p) = n.
%C A078928 A Pythagorean triangle is a right triangle whose edge lengths are all integers; such a triangle is 'primitive' if the lengths are relatively prime.
%C A078928 Least perimeter common to exactly n primitive Pythagorean triangles. - _Lekraj Beedassy_, May 14 2004
%H A078928 Derek J. C. Radden and Peter T. C. Radden, <a href="/A078928/b078928.txt">Table of n, a(n) for n=1..39</a> (terms 1 through 15 were computed by Derek J. C. Radden)
%H A078928 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_23">Number Curiosities</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 23, 567-604.
%H A078928 C. B. T. (Reviewer), <a href="https://www.jstor.org/stable/2002617">Review of Andrew S. Anema, A table of primitive Pythagorean triangle with identical perimeters</a>, Mathematical Tables and Other Aids to Computation, Vol. 10, No. 53 (Jan., 1956), pp. 35-36.
%e A078928 a(2)=1716; the primitive Pythagorean triangles with edge lengths (364, 627, 725) and (195, 748, 773) both have perimeter 1716.
%t A078928 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[per=2, True, per+=2, If[ct[per]==n, Return[per]]]
%Y A078928 a(n) = 2*A078927(n). Cf. A070109.
%K A078928 nonn
%O A078928 1,1
%A A078928 _Dean Hickerson_, Dec 15 2002
%E A078928 a(8) from _Robert G. Wilson v_, Dec 19 2002
%E A078928 a(9)-a(15) from _Derek J C Radden_, Dec 22 2012
%E A078928 a(16)-a(39) from _Peter T. C. Radden_, Dec 29 2012