%I A135202
%S A135202 3900,39000,390000
%N A135202 Numbers n that raised to the powers from 1 to k (with k>=1) are multiple 
               of the sum of their digits (n raised to k+1 must not be a multiple). 
               Case k=17.
%e A135202 3900^1=3900 is multiple of Sum_digits(3780)=12
%e A135202 3900^2=15210000 is multiple of Sum_digits(3600)=9
%e A135202 ...
%e A135202 3900^17 is a multiple of Sum_digits(3900^17)=108
%e A135202 while
%e A135202 3900^18 is not multiple of Sum_digits(3900^18)=99
%p A135202 readlib(log10); P:=proc(n,m) local a,i,k,w,x,ok; for i from 1 by 1 to 
               n do a:=simplify(log10(i)); if not (trunc(a)=a) then ok:=1; x:=1; 
               while ok=1 do w:=0; k:=i^x; while k>0 do w:=w+k-(trunc(k/10)*10); 
               k:=trunc(k/10); od; if trunc(i^x/w)=i^x/w then x:=x+1; else if x-1=m 
               then print(i); fi; ok:=0; fi; od; fi; od; end: P(50000,17);
%Y A135202 Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, 
               A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135201.
%Y A135202 Sequence in context: A108005 A065696 A014891 this_sequence A115468 A066386 
               A068240
%Y A135202 Adjacent sequences: A135199 A135200 A135201 this_sequence A135203 A135204 
               A135205
%K A135202 easy,nonn,base,bref
%O A135202 1,1
%A A135202 Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Nov 26 2007