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%I #10 May 27 2023 19:16:04
%S 34,74,290,650,1802,3530,7202,10370,20810,23330,38090,45002,64802,
%T 73730,78410,103970,115202,145802,159050,194690,242210,352802,373250,
%U 426890,544970,649802,720002,763850,824330,871202,1312202,1351370
%N Hypotenuses of special Pythagorean triples constructed from twin primes as follows: {u, w}={p,p+2}; side a=2p(p+2), side b=(p+2)^2-p^2 and the terms of sequence are values of c=a(n)=p^2+(p+2)^2=phi(a/2)+1+sigma(a/2)+1.
%C Sum of the numbers on the corners of the square array that lists the numbers from 1..A014574(n)^2 in increasing order by rows. - _Wesley Ivan Hurt_, May 27 2023
%F a(n) = 2 + A000203(A037074(n)) + A000010(A037074(n)) = A001359(n)^2 + A006512(n)^2.
%F a(n) = 2*(A014574(n)^2 + 1). - _Wesley Ivan Hurt_, May 27 2023
%e a(6) is obtained as follows: u = p = 41, w = p+2 = 43; a = 2*41*43 = 2*1763 = 3526; b = 43*2-41^2 = 1849-1681 = 168; c = 43^2+41^2 = 1849+1681 = 3530 = 1+phi(1763)+1+sigma(1763) = 1680+1848+2 = a(6); and 3526^2+168^2 = 3530^2.
%Y Cf. A001359, A006512, A000010, A000203, A014574, A037074, A063530-A063532.
%K nonn
%O 1,1
%A _Labos Elemer_, Aug 02 2001
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