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

Author

J. M. Bergot, Apr 23 2007

Keywords

• nonn
• base

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.

Examples

			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.
		

Crossrefs

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

Programs

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)&&(1M. F. Hasler, Apr 14 2015

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