A380193 a(n) is the largest number whose sixth power is an n-digit sixth power which has the maximum sum of digits (A373994(n)).

1, 2, 3, 4, 6, 7, 12, 19, 31, 46, 68, 96, 143, 206, 304, 461, 677, 977, 1194, 2136, 2896, 4633, 6373, 9763, 13817, 21542, 30643, 43693, 68123, 99812, 144083, 183967, 311296, 463976, 681017, 994333, 1441977, 2150104, 3022731, 4608562, 6765526, 9258023

Offset: 1

Author

Zhining Yang, Jan 15 2025

Keywords

• nonn
• base

Examples

			a(11) = 68 because among all 11-digit sixth powers(47^6-68^6), 64^6=68719476736 and 68^6=98867482624 have the maximum sum of digits, 96 = A373994(11) and 68 is the largest number.
		

Links

• Zhining Yang, Table of n, a(n) for n = 1..55 [a(47) corrected by _Kevin Ryde_, Mar 25 2025]

Crossrefs

Cf. A373994, A380567.

Other powers: A379298, A380052, A380797, A380566.

Programs

C

/* See A373994. */

Mathematica

Table[t=SortBy[Map[{#,Total@IntegerDigits[#^6]}&,Range[Ceiling[10^((n-1)/6)],Floor[(10^n-1)^(1/6)]]],Last];
Select[t,#[[2]]==t[[-1]][[2]]&][[1,1]],{n,36}]