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A023106 a(n) is a power of the sum of its digits. 5

%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 Base-10 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 base-10 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/mathematics-in-jack-reacher-novel.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_

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Last modified April 7 19:49 EDT 2020. Contains 333306 sequences. (Running on oeis4.)