OFFSET
1,1
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
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = 0 for n in A003635.
EXAMPLE
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.
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 *)
PROG
(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; }
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Michel Marcus, Oct 06 2016
STATUS
approved