A061988 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.

1, 3, 4, 3, 4, 5, 30, 120, 272, 315, 19, 43, 46, 47, 67

Offset: 1

Author

Frank Ellermann, May 26 2001

Keywords

• nonn
• tabl
• hard
• more
• nice

Examples

			Rows: (1), (3, 4), (3, 4, 5), (30, 120, 272, 315), (19, 43, 46, 47, 67), ...
		

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
• David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, NY, 1986, p. 164.

Crossrefs

A007666 gives values of k.

Extensions

Corrected by Vladeta Jovovic, 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.