cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A341432 a(n) is the denominator of the asymptotic density of numbers divisible by their last digit in base n.

This page as a plain text file.
%I A341432 #14 Nov 16 2022 15:02:24
%S A341432 2,2,12,12,60,20,840,840,2520,2520,27720,27720,360360,360360,720720,
%T A341432 720720,12252240,4084080,232792560,77597520,33256080,5173168,
%U A341432 5354228880,356948592,3824449200,26771144400,11473347600,80313433200,332727080400,2329089562800,144403552893600
%N A341432 a(n) is the denominator of the asymptotic density of numbers divisible by their last digit in base n.
%C A341432 a(n) divides A003418(n), and a(n) = A003418(n) for n = 1, 2, 4, 6, 8, 10, 12, ...
%H A341432 Amiram Eldar, <a href="/A341432/b341432.txt">Table of n, a(n) for n = 2..2300</a>
%F A341432 A341431(n)/a(n) = (1/n) * Sum_{k=1..n-1} gcd(k, n)/k. [corrected by _Amiram Eldar_, Nov 16 2022]
%F A341432 a(prime(n)) = A185399(n), for n > 1.
%e A341432 For n=2, the numbers divisible by their last binary digit are the odd numbers (A005408) whose density is 1/2, therefore a(2) = 2.
%e A341432 For n=3, the numbers divisible by their last digit in base 3 are the numbers that are congruent to {1, 2, 4} mod 6 (A047236) whose density is 1/2, therefore a(3) = 2.
%e A341432 For n=10, the numbers divisible by their last digit in base 10 are A034709 whose density is 1177/2520, therefore a(10) = 2520.
%t A341432 a[n_] := Denominator[Sum[GCD[k, n]/k, {k, 1, n - 1}]/n]; Array[a, 32, 2]
%Y A341432 Cf. A003418, A005408, A034709, A047236, A185399, A341431 (numerators).
%K A341432 nonn,base,frac,easy
%O A341432 2,1
%A A341432 _Amiram Eldar_, Feb 11 2021