cp's OEIS Frontend

A261315 Number of n-digit positive numbers whose digits occur with equal frequency.

%I A261315 #13 May 20 2025 08:12:32
%S A261315 9,90,657,4788,27225,146619,544329,2112084,3447369,28995255,9,
%T A261315 1488185631,9,73556822205,38222232057,3321970172244,9,138479121435807,
%U A261315 9,2209806802214163,19711054740199689,28570005,9,15574715941421647071,141378216540777225,421224309,9724427617362202602009
%N A261315 Number of n-digit positive numbers whose digits occur with equal frequency.
%C A261315 a(n) is divisible by 9.
%C A261315 a(n) = 9 if n > 10 is prime.
%H A261315 Robert Israel, <a href="/A261315/b261315.txt">Table of n, a(n) for n = 1..919</a>
%F A261315 a(n) = (9/10) * Sum_{j | n, j <= 10} n! * ((n/j)!)^(-j) * binomial(10,j).
%e A261315 For n = 1 there are the numbers 1 to 9.
%e A261315 For n = 2 there are 9 two-digit numbers of the form dd and 81 with two distinct digits, for a total of 90.
%e A261315 For n = 3 there are 9 numbers of the form ddd and 648 with three distinct digits, for a total of 657.
%e A261315 For n = 4 there are 9 numbers of the form dddd, 243 with two distinct digits each occurring twice, and 4536 with four distinct digits, for a total of 4788.
%p A261315 seq(9/10*add(n!/(n/j)!^j * binomial(10,j), j = select(`<=`,numtheory:-divisors(n),10)),n=1..30);
%Y A261315 Cf. A052060.
%K A261315 nonn,base
%O A261315 1,1
%A A261315 _Robert Israel_, Aug 14 2015