A135195 - OEIS

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

%S 6,330,360,1230,1440,2250,2490,2970,3150,3300,3600,4410,5010,5310,

%T 6930,8460,10020,12300,12840,12852,13050,14400,14700,15420,15840,

%U 16500,17220,18480,20010,21840,22500,23310,24840,24900,27702,28050,29610,29700,31500

%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=10.

%F Positive integers n such that A195860(n)=11.

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

%e 6^2=36 is a multiple of Sum_digits(36)=9

%e 6^3=216 is a multiple of Sum_digits(216)=9

%e 6^4=1296 is a multiple of Sum_digits(1296)=18

%e 6^5=7776 is a multiple of Sum_digits(7776)=27

%e 6^6=46656 is a multiple of Sum_digits(46656)=27

%e 6^7=279936 is a multiple of Sum_digits(279936)=36

%e 6^8=1679616 is a multiple of Sum_digits(1679616)=36

%e 6^9=10077696 is a multiple of Sum_digits(10077696)=36

%e 6^10=60466176 is a multiple of Sum_digits(60466176)=36

%e 6^11=362797056 is not a multiple of Sum_digits(362797056)=45

%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(15000,10);

%Y Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135196, A135197, A135198, A135199, A135200, A135201, A135202.

%K nonn,base

%O 1,1

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

%E Example corrected by _Paolo P. Lava_, Oct 23 2009

%E More terms from _Max Alekseyev_, Sep 24 2011