A124359 Numbers n for which the sum of the digits of n^k, for some k, is equal to n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 17, 18, 20, 22, 25, 26, 27, 28, 31, 34, 35, 36, 40, 43, 45, 46, 53, 54, 58, 63, 64, 68, 71, 80, 81, 82, 85, 86, 90, 91, 94, 97, 98, 103, 104, 106, 107, 108, 117, 118, 126, 127, 133, 134, 135, 136, 140, 142, 143, 146, 152, 154, 155, 157, 160, 163, 169, 170

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 27 2006

Keywords

• nonn
• base

Comments

Most of the values are conjectural. So far not much is proved about the function A247889. - M. F. Hasler and Robert Israel, May 18 2017

Examples

			18^3 = 5832 and 5 + 8 + 3 + 2 = 18 (also 18^6 = 34012224 and 18^7 = 612220032).
Again 46^5 = 205962976 and 2 + 0 + 5 + 9 + 6 + 2 + 9 + 7 + 6 = 46.
		

Links

• Hans Havermann, Table of n, a(n) for n = 1..3600
• Hans Havermann, Solutions (k) for the terms (n <= 20034) of this sequence

Crossrefs

Complement of A124367. Numbers for which A247889 is nonzero.

Programs

PARI

for(n=0,199,if(A247889(n),print1(n,", "))) \\ Derek Orr, Sep 25 2014

PARI

select(A247889,[0..170]) \\ M. F. Hasler, May 18 2017

Extensions

Prepended a(1) = 0, offset corrected and more terms added by Derek Orr, Sep 25 2014

Edited by M. F. Hasler, May 18 2017