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

1,2

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.

Links

Table of n, a(n) for n=1..15.

Example

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

Crossrefs

A007666 gives values of k.

Sequence in context: A220196 A128200 A258168 * A094151 A135800 A178152

Adjacent sequences: A061985 A061986 A061987 * A061989 A061990 A061991

Keyword

nonn,tabl,hard,more,nice

Author

Frank Ellermann, May 26 2001

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.

Status

approved