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

Author

Reinhard Zumkeller, Mar 19 2008

Keywords

• nonn
• base
• look

Comments

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

a(A051885(n)) = 0.

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

Examples

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

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

Crossrefs

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

Programs

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 *)

PARI

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