The On-Line Encyclopedia of Integer Sequences (OEIS)

A088307 revision #8

A088307

Triangle read by rows, 1 <= k <= n: T(n,k) = n^2 + k^2 if gcd(n,k)=1, otherwise 0.

0, 5, 0, 10, 13, 0, 17, 0, 25, 0, 26, 29, 34, 41, 0, 37, 0, 0, 0, 61, 0, 50, 53, 58, 65, 74, 85, 0, 65, 0, 73, 0, 89, 0, 113, 0, 82, 85, 0, 97, 106, 0, 130, 145, 0, 101, 0, 109, 0, 0, 0, 149, 0, 181, 0, 122, 125, 130, 137, 146, 157, 170, 185, 202, 221, 0, 145, 0, 0, 0, 169

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OFFSET

1,2

COMMENTS

(n^2-k^2, 2*k*n, T(n,k)) is a primitive Pythagorean triple iff T(n,k) > 0;

n > 1: T(n,1)=A002522(n); n > 0: T(2*n+1,2) = A078370(n); T(n,n)=0;

sum of n-th row = phi(n): A000010(n) = #{m: 1<=k<=n and T(n,m)>0} = Sum_{k=1..n} A057427(T(n,m)).

LINKS

Table of n, a(n) for n=1..71.

Eric Weisstein's World of Mathematics, Pythagorean Triple

EXAMPLE

n=6, k=5: 6^2 + 5^2 = 36 + 25 = 61: (6^2 - 5^2)^2 + (2*6*5)^2 = 11^2 + 60^2 = 121 + 3600 = 3721 = 61^2 = T(6,5)^2;