A138471 Number of numbers less than n having the same sum of digits.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 3, 3, 3, 3, 3, 3, 3, 2, 1, 0, 4, 4, 4, 4, 4, 4, 3, 2, 1, 0, 5, 5, 5, 5, 5, 4, 3, 2, 1, 0, 6, 6, 6, 6, 5, 4, 3, 2, 1, 0, 7, 7, 7, 6, 5, 4, 3, 2, 1, 0, 8, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 2, 3, 4, 5, 6

Offset

0,21

Comments

A138470(n) + a(n) + A138472(n) = n;

a(A051885(n)) = 0.

a(A228915(n)) = a(n)+1. - Robert Israel, May 26 2017

Links

Robert Israel, Table of n, a(n) for n = 0..10000 (terms 0..1500 from Reinhard Zumkeller)

Index entries for Colombian or self numbers and related sequences

Example

a(42)=#{6,15,24,33}=4.

Maple

N:= 1000: # to get a(0) to a(N)
C:= Vector(9*(1+ilog10(N))):
A[0]:= 0:
for n from 1 to N do
  s:= convert(convert(n, base, 10), `+`);
  A[n]:= C[s];
  C[s]:= C[s]+1;
od:
seq(A[i], i=0..N); # Robert Israel, May 25 2017

Mathematica

Module[{nn=110, sd}, sd=Total[IntegerDigits[#]]&/@Range[nn]; Join[{0}, Table[ Count[Take[sd, i-1], sd[[i]]], {i, nn}]]] (* Harvey P. Dale, Aug 14 2013 *)

Prog

(PARI) a(n) = my(sdn=sumdigits(n)); sum(k=1, n-1, sumdigits(k) == sdn); \\ Michel Marcus, May 26 2017

Crossrefs

Cf. A007953, A051885, A138470, A138472, A228915.

Sequence in context: A263204 A194322 A052010 * A102669 A248327 A055098

Adjacent sequences: A138468 A138469 A138470 * A138472 A138473 A138474

Keyword

nonn,base,look

Author

Reinhard Zumkeller, Mar 19 2008

Status

approved