%I #18 Apr 12 2021 00:17:38

%S 29,766,4225,13124675,224688658

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

%C a(7) > 2*10^11. - _Jon E. Schoenfield_, Apr 11 2021

%H R. Alter, <a href="https://doi.org/10.1007/BFb0096461">Computations and generalizations on a remark of Ramanujan</a>, pp. 182-196 of "Analytic Number Theory (Philadelphia, 1980)", ed. M. I. Knopp, Lect. Notes Math., Vol. 899, 1981.

%e From _Jon E. Schoenfield_, Apr 11 2021: (Start)

%e a(2) = 29 = 1^2 + 1^2 + 1^2 + 1^2 + 5^2

%e = 1^2 + 1^2 + 3^2 + 3^2 + 3^2

%e = 1^2 + 2^2 + 2^2 + 2^2 + 4^2.

%e .

%e a(3) = 766 = 1^3 + 1^3 + 2^3 + 3^3 + 9^3

%e = 1^3 + 4^3 + 4^3 + 5^3 + 8^3

%e = 2^3 + 2^3 + 4^3 + 7^3 + 7^3.

%e .

%e a(4) = 4225 = 2^4 + 2^4 + 2^4 + 3^4 + 8^4

%e = 2^4 + 4^4 + 4^4 + 6^4 + 7^4

%e = 3^4 + 4^4 + 6^4 + 6^4 + 6^4.

%e .

%e a(5) = 13124675 = 1^5 + 9^5 + 10^5 + 20^5 + 25^5

%e = 2^5 + 5^5 + 12^5 + 23^5 + 23^5

%e = 16^5 + 19^5 + 20^5 + 20^5 + 20^5.

%e .

%e a(6) = 224688658 = 3^6 + 8^6 + 19^6 + 20^6 + 22^6

%e = 5^6 + 5^6 + 16^6 + 16^6 + 24^6

%e = 8^6 + 10^6 + 15^6 + 20^6 + 23^6. (End)

%Y Cf. A230563, A342893-A342903.

%K nonn,hard,more

%O 2,1

%A _N. J. A. Sloane_, Apr 04 2021

%E a(6) from _Jinyuan Wang_, Apr 11 2021