A230563 Smallest number that is the sum of three positive n-th powers in at least two ways.

5, 27, 251, 2673, 1375298099, 160426514

Offset

1,1

Comments

a(7) > 10^26 (if it exists). - Donovan Johnson, Nov 22 2013

a(7) > 33055^7 ~ 4.31*10^31 (if it exists). Duncan Moore, Oct 07 2017

References

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, section 21.11.

Links

Table of n, a(n) for n=1..6.

R. Alter, Computations and generalizations on a remark of Ramanujan, pp. 182-196 of "Analytic Number Theory (Philadelphia, 1980)", ed. M. I. Knopp, Lect. Notes Math., Vol. 899, 1981. The value for a(6) given in Table 5 is wrong.

Example

5 = 1^1 + 1^1 + 3^1 = 1^1 + 2^1 + 2^1.
27 = 1^2 + 1^2 + 5^2 = 3^2 + 3^2 + 3^2.
251 = 1^3 + 5^3 + 5^3 = 2^3 + 3^3 + 6^3.
2673 = 2^4 + 4^4 + 7^4 = 3^4 + 6^4 + 6^4.
1375298099 = 3^5 + 54^5 + 62^5 = 24^5 + 28^5 + 67^5.
160426514 = 3^6 + 19^6 + 22^6 = 10^6 + 15^6 + 23^6.

Crossrefs

Cf. A046093, A230477, A230561, A230562.

Sequence in context: A376587 A356538 A342904 * A204266 A266204 A360770

Adjacent sequences: A230560 A230561 A230562 * A230564 A230565 A230566

Keyword

hard,more,nice,nonn

Author

Jonathan Sondow, Oct 25 2013

Extensions

a(4) and a(5) corrected by Donovan Johnson, Oct 28 2013

Edited by N. J. A. Sloane, Apr 03 2021

Status

approved