A052489 Largest number that is n times sum of its decimal digits.

0, 9, 18, 27, 48, 45, 54, 84, 72, 81, 90, 198, 108, 195, 126, 135, 288, 153, 162, 399, 180, 378, 396, 207, 216, 375, 468, 486, 588, 261, 270, 558, 576, 594, 408, 315, 648, 999, 684, 351, 480, 738, 756, 774, 792, 405, 966, 846, 864, 882, 450, 918, 936, 954

Offset: 0

Author

Henry Bottomley, Mar 16 2000

Keywords

• base
• nonn
• nice
• look
• changed

Comments

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

There are, however, positive n for which no positive number is n times the sum of its digits, in which case a(n) = 0, as for n = 62, 63, 65, 75, 84, ..., cf. A003635. - M. F. Hasler, Aug 24 2025

Links

• Daniel Mondot, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A003634, A003635, A052490.

Programs

Mathematica

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 *)

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