A216656 Number of n-digit 6th powers.

2, 1, 1, 1, 2, 3, 5, 7, 10, 15, 22, 31, 47, 69, 101, 148, 217, 318, 468, 687, 1008, 1479, 2171, 3187, 4678, 6867, 10078, 14793, 21714, 31870, 46780, 68664, 100784, 147931, 217134, 318707, 467800, 686635, 1007843, 1479311, 2171332, 3187079, 4677993, 6866354

Offset: 1

Author

Alois P. Heinz, Sep 12 2012

Keywords

• nonn
• base

Comments

a(6*k+1) + a(6*k+2) + a(6*k+3) + a(6*k+4) + a(6*k+5) + a(6*k+6) = 9*10^k for k >= 1. - Robert Israel, Jul 22 2018

Examples

			a(1) = 2: 0, 1.
a(2) = 1: 64.
a(3) = 1: 729.
a(4) = 1: 4096.
a(5) = 2: 15625, 46656.
a(6) = 3: 117649, 262144, 531441.
a(7) = 5: 1000000, 1771561, 2985984, 4826809, 7529536.
a(8) = 7: 11390625, 16777216, 24137569, 34012224, 47045881, 64000000, 85766121.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Column k=6 of A216653.

Programs

Maple

r:= proc(n, k) local b; b:= iroot(n, k); b+`if`(b^k r(10^n, 6) -r(10^(n-1), 6) +`if`(n=1, 1, 0):
seq(a(n), n=1..50);