%I #32 Aug 11 2023 16:20:54

%S 0,105,164,186,194,206,216,231,254,282,285,302,314,324,374,386,402,

%T 416,456,468,491,504,521,552,588,606,610,615,629,651,656,657,696,759,

%U 794,830,842,854,870,903,906,954,956,981,998,1029,1064,1079,1082,1109,1112,1131

%N Numbers k such that m=1 is the only number for which the sum of digits of m^k equals m.

%H Carole Dubois, <a href="/A133509/b133509.txt">Table of n, a(n) for n = 1..226</a> (terms 1..100 from Michael S. Branicky)

%H Carole Dubois, <a href="/A133509/a133509.jpg">Pin plot of A133509</a>

%F If t is a term, A046000(t)=1, A046017(t)=0, A046019(t)=1, A046471(t)=0 and A061211(t)=1. - _Mohammed Yaseen_, Jun 29 2022

%o (Python)

%o def ok(n):

%o d, lim = 1, 1

%o while lim < n*9*d: d, lim = d+1, lim*10

%o return not any(sum(map(int, str(k**n))) == k for k in range(2, lim+1))

%o for k in range(195):

%o if ok(k): print(k, end=", ") # _Michael S. Branicky_, Jul 06 2022

%Y Cf. A046000, A046017, A046019, A046471, A061211, A152147.

%K nonn,base

%O 1,2

%A _Farideh Firoozbakht_, Dec 04 2007

%E Description improved by _T. D. Noe_, Nov 26 2008

%E Extension by _T. D. Noe_, Nov 26 2008

%E Edited by _Charles R Greathouse IV_, Aug 02 2010

%E a(1) = 0 and a(46) and beyond from _Michael S. Branicky_, Jul 06 2022