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A342895
Smallest number that is the sum of five positive n-th powers in three ways.
2
29, 766, 4225, 13124675, 224688658
OFFSET
2,1
COMMENTS
a(7) > 2*10^11. - Jon E. Schoenfield, Apr 11 2021
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.
EXAMPLE
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)
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
N. J. A. Sloane, Apr 04 2021
EXTENSIONS
a(6) from Jinyuan Wang, Apr 11 2021
STATUS
approved