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

Author

Jonathan Sondow, Oct 25 2013

Keywords

• hard
• more
• nice
• nonn

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

Examples

			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.
		

References

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

Links

• 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.

Crossrefs

Cf. A046093, A230477, A230561, A230562.

Extensions

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

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