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Search: id:A088307
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| A088307 |
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T(n,k) = if GCD(n,k)=1 then n^2 + k^2 else 0: triangle read by rows, 1<=k<=n. |
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1
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| 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
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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(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(A057427(T(n,m)): 1<=k<=n).
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LINKS
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Eric Weisstein's World of Mathematics, Pythagorean Triple
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EXAMPLE
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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;
n=7, k=3: 7^2 + 3^2 = 49 + 9 = 58: (7^2 - 3^2)^2 + (2*7*3)^2 =
40^2 + 42^2 = 1600 + 1764 = 3364 = 58^2 = T(7,3)^2.
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CROSSREFS
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Cf. A070216.
Adjacent sequences: A088304 A088305 A088306 this_sequence A088308 A088309 A088310
Sequence in context: A101115 A010481 A022898 this_sequence A007392 A052401 A024418
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KEYWORD
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nonn,tabl
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 05 2003
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