A130180 Number of numbers k > 1 such that (sum of digits of k^n)*(sum of digits of k^(n+1)) = k.

5, 3, 12, 2, 6, 8, 4, 1, 13, 8, 7, 14, 8, 3, 9, 1, 5, 12, 4, 0, 13, 4, 7, 7, 1, 4, 7, 2, 5, 8, 2, 4, 8, 7, 1, 10, 5, 2, 8, 4, 2, 10, 2, 6, 10, 2, 3, 6, 2, 4, 4, 2, 3, 9, 2, 3, 8, 1, 3, 8, 5, 3, 6, 4, 6, 8, 4, 3, 10, 0, 1, 6, 3, 6, 6, 4, 2, 7, 2, 1

Offset: 1

Author

Klaus Brockhaus, May 14 2007

Keywords

• nonn
• base
• hard

Examples

			80, 1036, 1215 are the only numbers k > 1 such that (sum of digits of k^2)*(sum of digits of k^3) = k, hence a(2) = 3.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 1..116

Crossrefs

Cf. A126783 (smallest k), A130179 (upper bound), A130181 (largest k).

Extensions

a(55)-a(80) and b-file from Lars Blomberg, Dec 11 2011