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

1,3

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

Links

Hans Havermann, Table of n, a(n) for n = 1..3600

Hans Havermann, Solutions (k) for the terms (n <= 20034) of this sequence

Example

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.

Prog

(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

Crossrefs

Complement of A124367. Numbers for which A247889 is nonzero.

Sequence in context: A179977 A326298 A372281 * A124366 A289868 A304247

Adjacent sequences: A124356 A124357 A124358 * A124360 A124361 A124362

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 27 2006

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

Status

approved