A062933 Numbers k such that k divides the sum of digits of 8^k.

1, 2, 25, 70, 106, 268, 304, 358, 1559, 2369, 2824, 2855, 3616, 5218

Offset: 1

Author

Shyam Sunder Gupta and Amarnath Murthy, Feb 16 2002

Keywords

• hard
• nonn
• base

Comments

The next term, if it exists, is greater than 100000. - Ryan Propper, Aug 31 2005

No further terms less than 1000000 using the same method Donovan Johnson explains in A175525.

Examples

			25 divides the sum of digits of 8^25 (i.e., 3+7+7+7+8+9+3+1+8+6+2+9+5+7+1+6+1+7+0+9+5+6+8 = 125), so 25 is in the sequence.
		

Programs

Mathematica

k = 1; Do[k *= 8; s = Plus @@ IntegerDigits[k]; If[Mod[s, n] == 0, Print[n]], {n, 1, 10^5}] (* Ryan Propper, Aug 31 2005 *)
Select[Range[6000],Mod[Total[IntegerDigits[8^#]],#]==0&] (* Harvey P. Dale, Dec 26 2024 *)

Extensions

Corrected and extended by Ryan Propper, Aug 31 2005

Edited by Jon E. Schoenfield, May 29 2010