cp's OEIS Frontend

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

%I A277223 #21 Oct 07 2016 05:51:57
%S A277223 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 A277223 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 A277223 18,18,9,9,15,9,9,18,0,0,17,0,18,12,9,9,12,18,18,26,27,0
%N A277223 a(n) = A052489(n)/n.
%C A277223 a(n) is the largest multiplier k such that m = k*n is n times the sum of its decimal digits.
%C A277223 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 A277223 Robert Israel, <a href="/A277223/b277223.txt">Table of n, a(n) for n = 1..10000</a>
%F A277223 a(n) = 0 for n in A003635.
%F A277223 a(n) = A007953(A052489(n)). - _Altug Alkan_, Oct 06 2016
%e A277223 a(2)=9 because m=2*9=18 is the largest m that is twice the sum of its decimal digits.
%e A277223 a(4)=12 because m=4*12=48 is the largest m that is four times the sum of its decimal digits.
%p A277223 N:= 200: # to get a(1) .. a(N)
%p A277223 A:= Vector(N):
%p A277223 for t from 1 while 9*(1+ilog10(t))*N >= t do
%p A277223    k:= convert(convert(t,base,10),`+`);
%p A277223    if t mod k = 0 and t <= N*k then
%p A277223       A[t/k]:= max(A[t/k],k)
%p A277223    fi
%p A277223 od:
%p A277223 convert(A,list); # _Robert Israel_, Oct 06 2016
%t A277223 Table[Last[Select[Range[10^(IntegerLength@ n + 2)], n Total@ IntegerDigits@ # == # &] /. {} -> {0}]/n, {n, 75}] (* _Michael De Vlieger_, Oct 06 2016 *)
%o A277223 (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 A277223 Cf. A003635, A052489.
%K A277223 nonn,base
%O A277223 1,1
%A A277223 _Michel Marcus_, Oct 06 2016