%I #14 Nov 26 2015 00:20:21
%S 2,20,72,80,84,108,112,156,198,200,216,324,351,378,504,522,558,612,
%T 684,738,800,902,918,936,972,1008,1011,1040,1098,1101,1212,1242,1368,
%U 1386,1416,1452,1602,1611,1656,1674,1818,1836,1908,1998,2000,2088,2178
%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=3.
%F Positive integers n such that A195860(n) = 4.
%e 20^1=20, sum_digits(20)=2, and 20 is a multiple of 2;
%e 20^2=400, sum_digits(400)=4, and 400 is a multiple of 4;
%e 20^3=8000, sum_digits(8000)=8, and 8000 is a multiple of 8;
%e 20^4=160000, sum_digits(160000)=7, and 160000 is not a multiple of 7.
%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(2000,3);
%Y Cf. A135186, A135187, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135201, A135202.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_ & _Giorgio Balzarotti_, Nov 22 2007
%E More terms from _Max Alekseyev_, Sep 24 2011