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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=9.
12

%I #7 Aug 24 2012 10:50:00

%S 240,270,450,630,840,1050,2340,2400,2610,2700,3024,3036,3990,4500,

%T 5292,6300,6390,8400,9990,10170,10500,17160,18330,23400,24000,26100,

%U 27000,30240,30360,31110,35070,39900,40140,40740,41340,41700,43170,43470,44880

%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=9.

%F Positive integers n such that A195860(n)=10.

%e 240^1=240 is a multiple of Sum_digits(240)=6.

%e 240^2=57600 is a multiple of Sum_digits(240)=18.

%e 240^3=13824000 is a multiple of Sum_digits(13824000)=18.

%e 240^4=3317760000 is a multiple of Sum_digits(3317760000)=27.

%e 240^5=796262400000 is a multiple of Sum_digits(796262400000)=36.

%e 240^6=191102976000000 is a multiple of Sum_digits(191102976000000)=36.

%e 240^7=45864714240000000 is a multiple of Sum_digits(45864714240000000)=45.

%e 240^8=11007531417600000000 is a multiple of Sum_digits(11007531417600000000)=36.

%e 240^9=2641807540224000000000 is a multiple of Sum_digits(2641807540224000000000)=45.

%e 240^10=634033809653760000000000 is not a multiple of Sum_digits(634033809653760000000000)=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(15000,9);

%Y Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135195, A135196, A135197, A135198, A135199, A135200, A135201, A135202.

%K nonn,base

%O 1,1

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

%E More terms from _Max Alekseyev_, Sep 24 2011