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.
%I A341431 #14 Nov 16 2022 15:02:43 %S A341431 1,1,7,5,37,7,421,347,1177,671,14939,6617,135451,140311,271681,143327, %T A341431 5096503,751279,91610357,24080311,9098461,830139,2188298491,77709491, %U A341431 925316723,6609819823,3567606143,10876020307,123417992791,300151059037,37903472946337,32271030591223 %N A341431 a(n) is the numerator of the asymptotic density of numbers divisible by their last digit in base n. %H A341431 Amiram Eldar, <a href="/A341431/b341431.txt">Table of n, a(n) for n = 2..2300</a> %F A341431 a(n)/A341432(n) = (1/n) * Sum_{k=1..n-1} gcd(k, n)/k. [corrected by _Amiram Eldar_, Nov 16 2022] %e A341431 The sequence of fractions begins with 1/2, 1/2, 7/12, 5/12, 37/60, 7/20, 421/840, 347/840, 1177/2520, 671/2520, 14939/27720, 6617/27720, 135451/360360, 140311/360360, ... %e A341431 For n=2, the numbers divisible by their last binary digit are the odd numbers (A005408) whose density is 1/2, therefore a(2) = 1. %e A341431 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) = 1. %e A341431 For n=10, the numbers divisible by their last digit in base 10 are A034709 whose density is 1177/2520, therefore a(10) = 1177. %t A341431 a[n_] := Numerator[Sum[GCD[k, n]/k, {k, 1, n - 1}]/n]; Array[a, 32, 2] %Y A341431 Cf. A005408, A034709, A047236, A341432 (denominators). %K A341431 nonn,base,frac,easy %O A341431 2,3 %A A341431 _Amiram Eldar_, Feb 11 2021