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%I #8 Aug 24 2012 10:50:00
%S 210,2100,2310,14490,21000,23100,100020,144900,210000,231000,397320,
%T 424830,1000200,1113420,1449000,2100000,2310000,3619770,3973200,
%U 4248300,5349960,5397000,7773150,8851920,10002000,11134200,12035100,14490000,15496740
%N 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=16.
%F Positive integers n such that A195860(n)=17.
%e 210^1=210 is multiple of Sum_digits(210)=3
%e 210^2=44100 is multiple of Sum_digits(44100)=9
%e ...
%e 210^16=14305686902419853283210000000000000000 is a multiple of Sum_digits(210^16)=90
%e while
%e 210^17=3004194249508169189474100000000000000000 is not multiple of Sum_digits(210^17)=99
%p 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(45000,16);
%Y Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135202.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Nov 26 2007
%E Terms a(7) onward from _Max Alekseyev_, Sep 24 2011
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