|
%I #9 Aug 24 2012 10:50:00
%S 90,120,900,1200,3480,4650,5700,7140,9000,12000,13140,13260,21180,
%T 21660,25320,28560,30720,33660,34800,41580,46500,57000,60690,71400,
%U 81420,88110,90000,108450,120000,131400,132600,145710,211800,216180,216600,224490
%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=12.
%F Positive integers n such that A195860(n)=13.
%e 90^1=90 is multiple of Sum_digits(90)=9
%e 90^2=8100 is multiple of Sum_digits(8100)=9
%e etc. till
%e 90^12=282429536481000000000000 is multiple of Sum_digits(282429536481000000000000)=54
%e while
%e 90^13=25418658283290000000000000 is not multiple of Sum_digits(25418658283290000000000000)=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(25000,12);
%Y Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135198, A135199, A135200, A135201, A135202.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Nov 23 2007
%E Terms a(15) onward from _Max Alekseyev_, Sep 24 2011
|
