A343081 a(n) is the smallest number that is the sum of n positive cubes in three or more ways.

5104, 1225, 766, 221, 222, 223, 224, 197, 163, 164, 165, 166, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177

Offset: 3

Author

Sean A. Irvine, Apr 04 2021

Keywords

• nonn
• easy

Comments

This is r(n,3,3) in Alter's notation.

Examples

			a(3) = 5104 = 1^3 + 12^3 + 15^3 = 2^3 + 10^3 + 16^3 = 9^3 + 10^3 + 15^3.
a(4) = 1225 = 1^3 + 2^3 + 6^3 + 10^3 = 3^3 + 7^3 + 7^3 + 8^3 = 4^3 + 6^3 + 6^3 + 9^3.
a(9) = 224 = 6^3 + 8*1^3 = 3*4^3 + 3^3 + 5*1^3 = 5^3 + 4^3 + 4*2^3 + 3*1^3.
		

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 7, page 192.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A342902, A343080, A343082, A343083, A343085.

Formula

a(n) = n + 124 for n >= 15.

Extensions

Corrected by Robert Israel, Apr 05 2021

a(9) reverted by Sean A. Irvine, Apr 18 2021