Search: id:A135198
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%I A135198
%S A135198 780,1890,4620,5040,7800,12360,18900,20610,22950
%N A135198 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=13.
%e A135198 780^1=780 is multiple of Sum_digits(780)=15
%e A135198 780^2=608400 is multiple of Sum_digits(608400)=18
%e A135198 etc. till
%e A135198 780^13=39557590922648009090580480000000000000 is a multiple of Sum_digits(39557590922648009090580480000000000\
               000)=117
%e A135198 while
%e A135198 780^14=30854920919665447090652774400000000000000 is not multiple of Sum_digits(308549209196654470906527744000\
               00000000000)=126
%p A135198 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(25000,13);
%Y A135198 Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, 
               A135194, A135195, A135196, A135197, A135199, A135200, A135201, A135202.
%Y A135198 Sequence in context: A043384 A008746 A147547 this_sequence A139400 A115467 
               A020231
%Y A135198 Adjacent sequences: A135195 A135196 A135197 this_sequence A135199 A135200 
               A135201
%K A135198 easy,nonn,base
%O A135198 1,1
%A A135198 Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Nov 23 2007

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