%I
%S 0,1,2,3,4,5,6,7,8,9,81,512,2401,4913,5832,17576,19683,234256,390625,
%T 614656,1679616,17210368,34012224,52521875,60466176,205962976,
%U 612220032,8303765625,10460353203,24794911296,27512614111,52523350144,68719476736
%N a(n) is a power of the sum of its digits.
%C Base10 Reacher numbers: named for the character Jack Reacher in the series of books by Lee Child. Reacher likes the number 81 because it is the square of the sum of its base10 digits.  _Jeffrey Shallit_, Apr 03 2015
%C Contains A061209 and A061210 and all terms of A061211. See A252648 for numbers which are the sum of some power of their digits.  _M. F. Hasler_, Apr 13 2015
%D Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 36.
%H David W. Wilson, <a href="/A023106/b023106.txt">Table of n, a(n) for n = 0..1137</a>
%H Jeffrey Shallit, <a href="http://recursed.blogspot.ca/2007/09/mathematicsinjackreachernovel.html">Mathematics in a Jack Reacher Novel</a>, blog post, September 8 2007.
%e 2401 is an element because 2401 = 7^4 is a power of its digit sum 7.
%t fQ[n_] := Block[{b = Plus @@ IntegerDigits[n]}, If[b > 1, IntegerQ[ Log[b, n]] ]]; Take[ Select[ Union[ Flatten[ Table[n^m, {n, 55}, {m, 9}]]], fQ[ # ] &], 31] (* _Robert G. Wilson v_, Jan 28 2005 *)
%o (PARI) is(n)={n<10(!(n%s=sumdigits(n))&&s>1&&n==s^round(log(n)/log(s)))} \\ _M. F. Hasler_, Apr 13 2015
%o (Python) import math
%o def is_valid(n): dsum = sum(map(int, str(n))); return dsum ** int(round(math.log(n, dsum))) == n if dsum > 1 else n < 2
%o # _Victor Dumbrava_, May 02 2018
%Y Cf. A061209, A061210, A061211, A252648.
%K nonn,base,nice
%O 0,3
%A _David W. Wilson_
