%I #14 Nov 26 2015 00:20:09
%S 4,5,7,8,27,40,50,70,81,114,133,135,152,153,171,192,195,209,222,224,
%T 225,228,230,247,261,266,280,285,308,312,320,322,336,364,370,372,375,
%U 392,399,400,405,407,408,410,423,440,444,448,465,481,500,511,512,516,518
%N Numbers n that raised to the powers from 1 to k (with k>=1) are multiples of the sums of their digits (and n raised to the power k+1 is not such a multiple). Case k=1.
%C The sequence is a subset of Niven (or Harshad) numbers A005349.
%F Positive integers n such that A195860(n) = 2.
%e 7 can be divided only for 7^1; 7^2 = 49, sum_digits(49) = 13, and 49 is not a multiple of 13.
%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(2000,1);
%Y Cf. A135187 - A135202.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_ & _Giorgio Balzarotti_, Nov 22 2007
%E Definition edited by _N. J. A. Sloane_, Sep 04 2010