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%I #32 Oct 08 2017 12:31:29
%S 0,9,18,27,48,45,54,84,72,81,90,198,108,195,126,135,288,153,162,399,
%T 180,378,396,207,216,375,468,486,588,261,270,558,576,594,408,315,648,
%U 999,684,351,480,738,756,774,792,405,966,846,864,882,450,918,936,954
%N Largest number that is n times sum of its decimal digits.
%C It is infinite, as pointed out by Dr. Geoffrey Landis: Clearly if you have one integer that is N times the sum of its decimal digits, then when you add a 0 to the end, you have an integer that is 10N times the sum of its decimal digits. - _Jonathan Vos Post_, Feb 06 2011
%H Daniel Mondot, <a href="/A052489/b052489.txt">Table of n, a(n) for n = 0..9999</a>
%t p[n_] := 10(Length[IntegerDigits[n]]+1); a[0]=0; a[n_] := Catch[For[k = p[n]*n, k >= 0, k--, If[k == n*Total[IntegerDigits[k]], If[k == 0, Print["a(", n, ") not found"]]; Throw[k]]]]; Table[a[n], {n, 0, 1000}] (* _Jean-François Alcover_, Jul 19 2012 updated Oct 06 2016 after _Daniel Mondot_'s observations *)
%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));); 0;} \\ _Michel Marcus_, Oct 05 2016
%Y Cf. A003634, A003635, A052490.
%K base,nonn,nice,look
%O 0,2
%A _Henry Bottomley_, Mar 16 2000
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