cp's OEIS Frontend

A329392 Ordered perimeters p of primitive Pythagorean triangles no side of which is squarefree.

%I A329392 #23 Jan 05 2020 12:14:37
%S A329392 286,1026,1702,1798,3286,3920,4508,5368,6042,6450,6466,6552,7686,7938,
%T A329392 8520,8964,9900,10044,10296,10324,10494,11988,13206,13612,13786,13806,
%U A329392 14058,14606,15004,15912,16692,17316,18382,18748,20002,20328,21054,22042,23074,24402,24926,25500,25872,26378,27104
%N A329392 Ordered perimeters p of primitive Pythagorean triangles no side of which is squarefree.
%C A329392 There are no perimeters p of primitive Pythagorean triangles all sides of which are squarefree. This is because one side is twice the product of two relatively prime numbers not both odd and therefore even.
%C A329392 Many terms of this sequence can be obtained by scaling (3,4,5) the sides of the smallest primitive Pythagorean triangle. For example, a(1) = (3*39) + (4*11) + (5*25).
%C A329392 a(6) is the first term of the sequence which cannot be obtained by scaling (3,4,5). In fact there is no primitive Pythagorean triangle smaller than a(6) that can be scaled to a(6) in the manner above, and in the context of this sequence a(6) can be thought of as "primitive".
%C A329392 a(514) = 310464 is the smallest perimeter corresponding to two triangles, namely (3^2*7^2*263, 2^6*11*89, 5^2*5273) and (2^6*3^2*251, 7^2*11*37, 5*17^2*101). - _Giovanni Resta_, Nov 15 2019
%C A329392 a(n) is the inner product of two vectors the components of which are relatively prime.
%e A329392 286 is a term because 286 = (2*2*11) + (3*3*13) + (5*5*5).
%e A329392 1026 is a term because 1026 = (3*3*3*11) + (2*2*2*2*19) + (5*5*17).
%e A329392 1702 is a term because 1702 = (3*3*37) + (2*2*7*23) + (5*5*29).
%Y A329392 Subset of A024364.
%K A329392 nonn
%O A329392 1,1
%A A329392 _Torlach Rush_, Nov 12 2019