A135191 - OEIS

%I #12 Nov 26 2015 05:47:07

%S 24,54,510,540,624,690,888,960,1110,1530,1710,1848,2010,2070,2142,

%T 2232,2604,2844,2916,4020,4230,4332,4488,4968,5100,5202,5280,5400,

%U 5550,5742,6420,6444,6630,6636,6660,6900,7350,7920,8190,8592,8610,8730

%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=6.

%F Positive integers n such that A195860(n)=7.

%e 24^1 = 24 -> Sum_digits(24) = 6, and 24 is a multiple of 6.

%e 24^2 = 576 -> Sum_digits(576) = 18, and 576 is a multiple of 18.

%e 24^3 = 13824 -> Sum_digits(13824) = 18, and 13824 is a multiple of 18.

%e 24^4 = 331776 -> Sum_digits(331776) = 27, and 331776 is a multiple of 27.

%e 24^5 = 7962624 -> Sum_digits(7962624) = 36, and 7962624 is a multiple of 36.

%e 24^6 = 191102976 -> Sum_digits(191102976) = 36, and 191102976 is a multiple of 36.

%e 24^7 = 4586471424 -> Sum_digits(4586471424) = 45, and 4586471424 is not a multiple of 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(2000,6);

%Y Cf. A135186 - 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