A277223 - OEIS

%I #21 Oct 07 2016 05:51:57

%S 9,9,9,12,9,9,12,9,9,9,18,9,15,9,9,18,9,9,21,9,18,18,9,9,15,18,18,21,

%T 9,9,18,18,18,12,9,18,27,18,9,12,18,18,18,18,9,21,18,18,18,9,18,18,18,

%U 18,18,9,9,15,9,9,18,0,0,17,0,18,12,9,9,12,18,18,26,27,0

%N a(n) = A052489(n)/n.

%C a(n) is the largest multiplier k such that m = k*n is n times the sum of its decimal digits.

%C a(n) is never 1, 2, 3, 4, 5 or 6. Conjecture: if a(n) < 12 then a(n) = 0 or 9. - _Robert Israel_, Oct 06 2016

%H Robert Israel, <a href="/A277223/b277223.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 0 for n in A003635.

%F a(n) = A007953(A052489(n)). - _Altug Alkan_, Oct 06 2016

%e a(2)=9 because m=2*9=18 is the largest m that is twice the sum of its decimal digits.

%e a(4)=12 because m=4*12=48 is the largest m that is four times the sum of its decimal digits.

%p N:= 200: # to get a(1) .. a(N)

%p A:= Vector(N):

%p for t from 1 while 9*(1+ilog10(t))*N >= t do

%p    k:= convert(convert(t,base,10),`+`);

%p    if t mod k = 0 and t <= N*k then

%p       A[t/k]:= max(A[t/k],k)

%p    fi

%p od:

%p convert(A,list); # _Robert Israel_, Oct 06 2016

%t Table[Last[Select[Range[10^(IntegerLength@ n + 2)], n Total@ IntegerDigits@ # == # &] /. {} -> {0}]/n, {n, 75}] (* _Michael De Vlieger_, Oct 06 2016 *)

%o (PARI) a(n) = {nbd = 1; while (9*nbd*n > 10^nbd, nbd++); forstep(k=9*nbd*n, 1, -1, if (sumdigits(k)*n == k, return(k/n));); 0;}

%Y Cf. A003635, A052489.

%K nonn,base

%O 1,1

%A _Michel Marcus_, Oct 06 2016