A063533 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.

34, 74, 290, 650, 1802, 3530, 7202, 10370, 20810, 23330, 38090, 45002, 64802, 73730, 78410, 103970, 115202, 145802, 159050, 194690, 242210, 352802, 373250, 426890, 544970, 649802, 720002, 763850, 824330, 871202, 1312202, 1351370

Offset: 1

Author

Labos Elemer, Aug 02 2001

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A001359, A006512, A000010, A000203, A014574, A037074, A063530-A063532.

Formula

a(n) = 2 + A000203(A037074(n)) + A000010(A037074(n)) = A001359(n)^2 + A006512(n)^2.

a(n) = 2*(A014574(n)^2 + 1). - Wesley Ivan Hurt, May 27 2023