A128912 Numbers m of the form (sum of digits of m)^k, k > 1.

0, 1, 81, 512, 2401, 4913, 5832, 17576, 19683, 234256, 390625, 614656, 1679616, 17210368, 34012224, 52521875, 60466176, 205962976, 612220032, 8303765625, 10460353203, 24794911296, 27512614111, 52523350144, 68719476736

Offset

1,3

Comments

Perfect powers m > 1 such that the sum of the digits of m equals one of its nontrivial roots.

Essentially a duplicate of A023106, where numbers 2 through 9 are allowed as solutions for k=1.

Links

Table of n, a(n) for n=1..25.

Example

234256 = 22^4 and 2+3+4+2+5+6 = 22, hence 234256 is a term.
390625 = 25^4 and 3+9+0+6+2+5 = 25, hence 390625 is a term.

Prog

(PARI) {m=10^5; z=10^11; v=[]; for(n=0, m, k=2; while((p=n^k)<=z, s=sumdigits(p); if(n==s, v=concat(v, p)); k++)); v=vecsort(v); print(v)} \\ Klaus Brockhaus, Apr 24 2007, edited by M. F. Hasler, Apr 14 2015
(PARI) is(n)=ispower(n)&&(1<s=sumdigits(n))&&n==s^round(log(n)/log(s))||n<2 \\ M. F. Hasler, Apr 14 2015

Crossrefs

Cf. A001597 (perfect powers), A007953 (sum of digits).

Sequence in context: A235531 A235527 A297122 * A076090 A183428 A236663

Adjacent sequences: A128909 A128910 A128911 * A128913 A128914 A128915

Keyword

nonn,base

Author

J. M. Bergot, Apr 23 2007

Extensions

Edited, corrected and extended by Klaus Brockhaus, Apr 24 2007

Definition simplified and initial terms 0, 1 added by M. F. Hasler, Apr 14 2015

Status

approved