A135196 - OEIS

%I #9 Aug 24 2012 10:50:00

%S 420,990,1680,4200,9900,12060,12870,13230,16800,17010,25500,33570,

%T 37380,42000,53250,65310,75810,80010,99000,102750,115710,117810,

%U 120600,128700,132300,143640,155430,168000,170100,187110,191610,211860,213180,219450

%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=11.

%F Positive integers n such that A195860(n)=12.

%e 420^1=420 is multiple of Sum_digits(420)=6

%e 420^2=176400 is multiple of Sum_digits(176400)=18

%e etc. till

%e 420^11=71736832111046860800000000000 is multiple of Sum_digits(71736832111046860800000000000)=72

%e while

%e 420^12=30129469486639681536000000000000 is not multiple of Sum_digits(30129469486639681536000000000000)=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(15000,11);

%Y Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135197, A135198, A135199, A135200, A135201, A135202.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Nov 23 2007

%E Terms a(9) onward from _Max Alekseyev_, Sep 24 2011