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A138471 Number of numbers less than n having the same sum of digits. 5

%I

%S 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,

%T 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,

%U 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

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

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

%C a(A051885(n)) = 0.

%C a(A228915(n)) = a(n)+1. - _Robert Israel_, May 26 2017

%H Robert Israel, <a href="/A138471/b138471.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1500 from Reinhard Zumkeller)

%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>

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

%p N:= 1000: # to get a(0) to a(N)

%p C:= Vector(9*(1+ilog10(N))):

%p A[0]:= 0:

%p for n from 1 to N do

%p s:= convert(convert(n,base,10),`+`);

%p A[n]:= C[s];

%p C[s]:= C[s]+1;

%p od:

%p seq(A[i],i=0..N); # _Robert Israel_, May 25 2017

%t 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 *)

%o (PARI) a(n) = my(sdn=sumdigits(n)); sum(k=1, n-1, sumdigits(k) == sdn); \\ _Michel Marcus_, May 26 2017

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

%K nonn,base,look

%O 0,21

%A _Reinhard Zumkeller_, Mar 19 2008

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Last modified October 20 10:23 EDT 2019. Contains 328257 sequences. (Running on oeis4.)