Search: id:A135194
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%I A135194
%S A135194 240,270,450,630,840,1050,2340,2400,2610,2700,3024,3036,3990,4500,5292,
%T A135194 6300,6390,8400,9990,10170,10500
%N A135194 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=9.
%e A135194 240^1=240 is a multiple of Sum_digits(240)=6.
%e A135194 240^2=57600 is a multiple of Sum_digits(240)=18.
%e A135194 240^3=13824000 is a multiple of Sum_digits(13824000)=18.
%e A135194 240^4=3317760000 is a multiple of Sum_digits(3317760000)=27.
%e A135194 240^5=796262400000 is a multiple of Sum_digits(796262400000)=36.
%e A135194 240^6=191102976000000 is a multiple of Sum_digits(191102976000000)=36.
%e A135194 240^7=45864714240000000 is a multiple of Sum_digits(45864714240000000)=45.
%e A135194 240^8=11007531417600000000 is a multiple of Sum_digits(11007531417600000000)=36.
%e A135194 240^9=2641807540224000000000 is a multiple of Sum_digits(2641807540224000000000)=45.
%e A135194 240^10=634033809653760000000000 is not a multiple of Sum_digits(634033809653760000000000)=63.
%p A135194 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(15000,9);
%Y A135194 Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, 
               A135195, A135196, A135197, A135198, A135199, A135200, A135201, A135202.
%Y A135194 Sequence in context: A100748 A072235 A121378 this_sequence A031173 A067373 
               A030638
%Y A135194 Adjacent sequences: A135191 A135192 A135193 this_sequence A135195 A135196 
               A135197
%K A135194 easy,nonn,base
%O A135194 1,1
%A A135194 Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Nov 23 2007

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