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A061988
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Find smallest k such that k^n is a sum of n n-th powers, say k^n = T(n,1)^n + .. + T(n,n)^n. Sequence gives triangle of successive rows T(n,1), ..., T(n,n). T(n,1) = .. = T(n,n) = 0 indicates no solution exists.
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1
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1, 3, 4, 3, 4, 5, 30, 120, 272, 315, 19, 43, 46, 47, 67
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, equation 21.11.2
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 164.
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EXAMPLE
| Rows: (1), (3, 4), (3, 4, 5), (30, 120, 272, 315), (19, 43, 46, 47, 67), ...
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CROSSREFS
| A007666 gives values of k.
Sequence in context: A052384 A100867 A128200 * A094151 A135800 A178152
Adjacent sequences: A061985 A061986 A061987 * A061989 A061990 A061991
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KEYWORD
| nonn,tabl,hard,nice
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AUTHOR
| Frank.Ellermann(AT)t-online.de, May 26 2001
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EXTENSIONS
| Corrected by Vladeta Jovovic (vladeta(AT)eunet.rs), May 29 2001
A few particular solutions are known for k = 4: 651^4 = 240^4 + 340^4 + 430^4 + 599^4, 5281^4 = 1000^4 + 1120^4 + 3233^4 + 5080^4, 7703^4 = 2230^4 + 3196^4 + 5620^4 + 6995^4,... The smallest one is 353^4 = 30^4 + 120^4 + 272^4 + 315^4.
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