cp's OEIS Frontend

A342899 Smallest number that is the sum of five positive n-th powers in four ways.

%I A342899 #19 May 09 2021 06:11:36
%S A342899 53,1252,20995,287618651,351060139210
%N A342899 Smallest number that is the sum of five positive n-th powers in four ways.
%H A342899 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 A342899 53 = 1^2 + 1^2 + 1^2 + 1^2 + 7^2
%e A342899    = 1^2 + 1^2 + 1^2 + 5^2 + 5^2
%e A342899    = 1^2 + 2^2 + 4^2 + 4^2 + 4^2
%e A342899    = 1^2 + 3^2 + 3^2 + 3^2 + 5^2
%e A342899    = 2^2 + 2^2 + 2^2 + 4^2 + 5^2.
%e A342899 1252 = 1^3 + 1^3 + 5^3 + 5^3 + 10^3
%e A342899      = 1^3 + 2^3 + 3^3 + 6^3 + 10^3
%e A342899      = 3^3 + 3^3 + 7^3 + 7^3 +  8^3
%e A342899      = 3^3 + 4^3 + 6^3 + 6^3 +  9^3.
%e A342899 20995 = 1^4 + 1^4 + 1^4 + 4^4 + 12^4
%e A342899       = 2^4 + 3^4 + 3^4 + 3^4 + 12^4
%e A342899       = 2^4 + 6^4 + 9^4 + 9^4 +  9^4
%e A342899       = 4^4 + 6^4 + 7^4 + 7^4 + 11^4.
%e A342899 287618651 =  8^5 + 21^5 + 27^5 + 27^5 + 48^5
%e A342899           =  9^5 + 13^5 + 26^5 + 37^5 + 46^5
%e A342899           = 11^5 + 12^5 + 23^5 + 41^5 + 44^5
%e A342899           = 11^5 + 20^5 + 22^5 + 30^5 + 48^5.
%e A342899 351060139210 =  8^6 + 50^6 + 53^6 + 56^6 + 81^6
%e A342899              = 18^6 + 43^6 + 49^6 + 64^6 + 80^6
%e A342899              = 27^6 + 31^6 + 56^6 + 62^6 + 80^6
%e A342899              = 35^6 + 36^6 + 38^6 + 73^6 + 76^6.
%Y A342899 Cf. A230563, A342893-A342903.
%K A342899 nonn,hard,more
%O A342899 2,1
%A A342899 _N. J. A. Sloane_, Apr 04 2021
%E A342899 a(5) from _Robert Israel_, Apr 07 2021
%E A342899 a(6) from _Michael S. Branicky_, May 08 2021