OFFSET
2,1
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
53 = 1^2 + 1^2 + 1^2 + 1^2 + 7^2
= 1^2 + 1^2 + 1^2 + 5^2 + 5^2
= 1^2 + 2^2 + 4^2 + 4^2 + 4^2
= 1^2 + 3^2 + 3^2 + 3^2 + 5^2
= 2^2 + 2^2 + 2^2 + 4^2 + 5^2.
1252 = 1^3 + 1^3 + 5^3 + 5^3 + 10^3
= 1^3 + 2^3 + 3^3 + 6^3 + 10^3
= 3^3 + 3^3 + 7^3 + 7^3 + 8^3
= 3^3 + 4^3 + 6^3 + 6^3 + 9^3.
20995 = 1^4 + 1^4 + 1^4 + 4^4 + 12^4
= 2^4 + 3^4 + 3^4 + 3^4 + 12^4
= 2^4 + 6^4 + 9^4 + 9^4 + 9^4
= 4^4 + 6^4 + 7^4 + 7^4 + 11^4.
287618651 = 8^5 + 21^5 + 27^5 + 27^5 + 48^5
= 9^5 + 13^5 + 26^5 + 37^5 + 46^5
= 11^5 + 12^5 + 23^5 + 41^5 + 44^5
= 11^5 + 20^5 + 22^5 + 30^5 + 48^5.
351060139210 = 8^6 + 50^6 + 53^6 + 56^6 + 81^6
= 18^6 + 43^6 + 49^6 + 64^6 + 80^6
= 27^6 + 31^6 + 56^6 + 62^6 + 80^6
= 35^6 + 36^6 + 38^6 + 73^6 + 76^6.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
N. J. A. Sloane, Apr 04 2021
EXTENSIONS
a(5) from Robert Israel, Apr 07 2021
a(6) from Michael S. Branicky, May 08 2021
STATUS
approved