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