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%I #12 Nov 25 2015 22:32:28
%S 3,12,36,42,102,162,432,468,1002,1026,1080,1188,1215,1380,1512,1620,
%T 1770,1950,1980,2136,2394,2460,2466,2628,3210,3240,3276,3492,3540,
%U 3654,3816,3864,4032,4050,4116,4374,4680,4752,4806,4860,4950,5058,5238
%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=5.
%F Positive integers n such that A195860(n)=6.
%e 3^1=3
%e 3^2=9 and 9 is a multiple of 3
%e 3^3=27 -> Sum_digits(27)=9 and 27 is a multiple of 9
%e 3^4=81 -> Sum_digits(81)=9 and 81 is a multiple of 9
%e 3^5=243 -> Sum_digits(243)=9 and 243 is a multiple of 9
%e 3^6=729 -> Sum_digits(729)=18 and 729 is not a multiple of 18
%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(2000,5);
%Y Cf. A135186, A135187, A135188, A135189, 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
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