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%I #13 Feb 18 2024 23:36:45
%S 0,1,81,512,2401,4913,5832,17576,19683,234256,390625,614656,1679616,
%T 17210368,34012224,52521875,60466176,205962976,612220032,8303765625,
%U 10460353203,24794911296,27512614111,52523350144,68719476736
%N Numbers m of the form (sum of digits of m)^k, k > 1.
%C Perfect powers m > 1 such that the sum of the digits of m equals one of its nontrivial roots.
%C Essentially a duplicate of A023106, where numbers 2 through 9 are allowed as solutions for k=1.
%e 234256 = 22^4 and 2+3+4+2+5+6 = 22, hence 234256 is a term.
%e 390625 = 25^4 and 3+9+0+6+2+5 = 25, hence 390625 is a term.
%o (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
%o (PARI) is(n)=ispower(n)&&(1<s=sumdigits(n))&&n==s^round(log(n)/log(s))||n<2 \\ _M. F. Hasler_, Apr 14 2015
%Y Cf. A001597 (perfect powers), A007953 (sum of digits).
%K nonn,base
%O 1,3
%A _J. M. Bergot_, Apr 23 2007
%E Edited, corrected and extended by _Klaus Brockhaus_, Apr 24 2007
%E Definition simplified and initial terms 0, 1 added by _M. F. Hasler_, Apr 14 2015