|
%I #16 Apr 01 2017 10:39:29
%S 126,480,660,810,882,1020,1134,1170,1260,1320,1560,1590,2022,3042,
%T 3222,4662,4800,5670,5940,6240,6600,7110,7452,8100,8442,8550,8820,
%U 8880,9510,10110,10200,10350,10620,10890,11010,11106,11130,11340,11460,11700,11970
%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=7.
%H Harvey P. Dale, <a href="/A135192/b135192.txt">Table of n, a(n) for n = 1..1000</a>
%F Positive integers n such that A195860(n) = 8.
%e 126^1 = 126 -> Sum_digits(126) = 9, and 126 is a multiple of 9
%e 126^2 = 15876 -> Sum_digits(15876) = 27, and 15876 is a multiple of 27
%e 126^3 = 2000376 -> Sum_digits(2000376) = 18, and 2000376 is a multiple of 18
%e 126^4 = 252047376 -> Sum_digits(252047376) = 36, and 252047376 is a multiple of 36
%e 126^5 = 31757969376 -> Sum_digits(31757969376) = 63, and 31757969376is a multiple of 63
%e 126^6 = 4001504141376 -> Sum_digits(4001504141376) = 36, and 4001504141376 is a multiple of 36
%e 126^7 = 504189521813376 -> Sum_digits(504189521813376) = 63, and 504189521813376 is a multiple of 63
%e 126^8 = 63527879748485376 -> Sum_digits(63527879748485376) = 99, and 63527879748485376 is not a multiple of 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(2000,7);
%t msdQ[n_]:=AllTrue[n^Range[7],Divisible[#,Total[IntegerDigits[#]]]&] && !Divisible[n^8,Total[IntegerDigits[n^8]]]; Select[Range[12000],msdQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Apr 01 2017 *)
%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
|
