%I #17 May 09 2024 09:08:38

%S 2,81,512,2401,17210368,34012224,612220032,20047612231936,

%T 3904305912313344,13744803133596058624,8007313507497959524352,

%U 2518170116818978404827136,81920000000000000,2670419511272061205254504361,2759031540715333904109053133443

%N Least number > 1 which equals n-th power of the sum of its digits in decimal base.

%H Michael De Vlieger, <a href="/A072408/b072408.txt">Table of n, a(n) for n = 1..274</a>

%H Leo Moser, Digits of Powers, Recreational Mathematics, Curiosa 145. <a href="https://dspace.bcu-iasi.ro/handle/123456789/43240">Scripta Mathematica Vol. XIII</a>, March-June 1947, Nos. 1-2, page 117.

%F a(n) = Min{ x; x=SumDigit(x)^n} = Min{x; x=A007953(x)^n}

%F a(n) = A046017(n)^n. - _Michael De Vlieger_, Nov 05 2020

%e a(1) = 2 > 1;

%e a(9) = 3904305912313344 = 54^9 = (3+9+0+4+3+0+5+9+1+2+3+1+3+3+4+4)^9.

%t Array[Block[{k = 2}, While[k^# != Total[IntegerDigits[k^#]]^#, k++]; k^#] &, 13] (* _Michael De Vlieger_, Nov 05 2020 *)

%Y Cf. A007953, A046017, A072081-A072083.

%K base,nonn

%O 1,1

%A _Labos Elemer_, Jun 17 2002