A343079 a(n) is the smallest number that is the sum of n positive 6th powers in two ways.

160426514, 1063010, 1063011, 570947, 570948, 63232, 63233, 52489, 52490, 52491, 16393, 16394, 16395, 16396, 16397, 13122, 13123, 13124, 13125, 13126, 13127, 13128, 13129, 13130, 13131, 13132, 13133, 13134, 13135, 13136, 13137, 13138, 8225, 8226, 8227, 8228, 8229, 6592, 6593, 6594, 6595, 6596, 6597, 6598, 6599, 6600, 6601, 6602, 6603, 6604, 6605, 6606, 6607, 6608, 6609, 6610, 6611, 6612, 6613, 6614, 6615, 6616, 4160

Offset: 3

Author

Sean A. Irvine, Apr 04 2021

Keywords

• nonn

Comments

This is r(n,6,2) in Alter's notation.

Alter paper has a typographical error a(3)=106426514.

Examples

			a(3) = 160426514 = 3^6 + 19^6 + 22^6 = 10^6 + 15^6 + 23^6.
a(4) = 1063010 = 2^6 + 2^6 + 9^6 + 9^6 = 3^6 + 5^6 + 6^6 + 10^6.
		

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. See Table 5, page 191.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A116643, A230563, A342902, A343077, A343078.

Formula

a(n) = n + 4095 for n >= 65.