A277223 a(n) = A052489(n)/n.

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

Offset: 1

Author

Michel Marcus, Oct 06 2016

Keywords

• nonn
• base

Comments

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

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

Examples

			a(2)=9 because m=2*9=18 is the largest m that is twice the sum of its decimal digits.
a(4)=12 because m=4*12=48 is the largest m that is four times the sum of its decimal digits.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003635, A052489.

Programs

Maple

N:= 200: # to get a(1) .. a(N)
A:= Vector(N):
for t from 1 while 9*(1+ilog10(t))*N >= t do
   k:= convert(convert(t,base,10),`+`);
   if t mod k = 0 and t <= N*k then
      A[t/k]:= max(A[t/k],k)
   fi
od:
convert(A,list); # Robert Israel, Oct 06 2016

Mathematica

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

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;}

Formula

a(n) = 0 for n in A003635.

a(n) = A007953(A052489(n)). - Altug Alkan, Oct 06 2016