A342895 Smallest number that is the sum of five positive n-th powers in three ways.

29, 766, 4225, 13124675, 224688658

Offset: 2

Author

N. J. A. Sloane, Apr 04 2021

Keywords

• nonn
• hard
• more

Comments

a(7) > 2*10^11. - Jon E. Schoenfield, Apr 11 2021

Examples

			From _Jon E. Schoenfield_, Apr 11 2021: (Start)
a(2) = 29 = 1^2 + 1^2 + 1^2 + 1^2 + 5^2
          = 1^2 + 1^2 + 3^2 + 3^2 + 3^2
          = 1^2 + 2^2 + 2^2 + 2^2 + 4^2.
.
a(3) = 766 = 1^3 + 1^3 + 2^3 + 3^3 + 9^3
           = 1^3 + 4^3 + 4^3 + 5^3 + 8^3
           = 2^3 + 2^3 + 4^3 + 7^3 + 7^3.
.
a(4) = 4225 = 2^4 + 2^4 + 2^4 + 3^4 + 8^4
            = 2^4 + 4^4 + 4^4 + 6^4 + 7^4
            = 3^4 + 4^4 + 6^4 + 6^4 + 6^4.
.
a(5) = 13124675 =  1^5 +  9^5 + 10^5 + 20^5 + 25^5
                =  2^5 +  5^5 + 12^5 + 23^5 + 23^5
                = 16^5 + 19^5 + 20^5 + 20^5 + 20^5.
.
a(6) = 224688658 = 3^6 +  8^6 + 19^6 + 20^6 + 22^6
                 = 5^6 +  5^6 + 16^6 + 16^6 + 24^6
                 = 8^6 + 10^6 + 15^6 + 20^6 + 23^6. (End)
		

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.

Crossrefs

Cf. A230563, A342893-A342903.

Extensions

a(6) from Jinyuan Wang, Apr 11 2021