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%I #14 Nov 26 2015 05:47:28
%S 180,252,720,1350,1800,2040,2520,3324,3870,5520,6552,6750,7200,7812,
%T 8220,8280,8964,9450,10080,10098,10980,12726,13500,13842,14130,14670,
%U 15120,15210,16170,16368,18000,18018,19170,19710,20040,20400,20538,20790
%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=8.
%F Positive integers n such that A195860(n) = 9.
%e 180^1 = 180 is a multiple of Sum_digits(180) = 9;
%e 180^2 = 32400 is a multiple of Sum_digits(32400) = 9;
%e 180^3 = 5832000 is a multiple of Sum_digits(5832000) = 18;
%e 180^4 = 1049760000 is a multiple of Sum_digits(1049760000) = 27;
%e 180^5 = 188956800000 is a multiple of Sum_digits(188956800000) = 45;
%e 180^6 = 34012224000000 is a multiple of Sum_digits(34012224000000) = 18;
%e 180^7 = 6122200320000000 is a multiple of Sum_digits(6122200320000000) = 18;
%e 180^8 = 1101996057600000000 is a multiple of Sum_digits(1101996057600000000) = 45;
%e 180^9 = 198359290368000000000 is not a multiple of Sum_digits(198359290368000000000) = 63.
%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(10000,8);
%Y Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135201, A135202.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_ & _Giorgio Balzarotti_, Nov 23 2007
%E More terms from _Max Alekseyev_, Sep 24 2011
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