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A341432
a(n) is the denominator of the asymptotic density of numbers divisible by their last digit in base n.
4
2, 2, 12, 12, 60, 20, 840, 840, 2520, 2520, 27720, 27720, 360360, 360360, 720720, 720720, 12252240, 4084080, 232792560, 77597520, 33256080, 5173168, 5354228880, 356948592, 3824449200, 26771144400, 11473347600, 80313433200, 332727080400, 2329089562800, 144403552893600
OFFSET
2,1
COMMENTS
a(n) divides A003418(n), and a(n) = A003418(n) for n = 1, 2, 4, 6, 8, 10, 12, ...
LINKS
FORMULA
A341431(n)/a(n) = (1/n) * Sum_{k=1..n-1} gcd(k, n)/k. [corrected by Amiram Eldar, Nov 16 2022]
a(prime(n)) = A185399(n), for n > 1.
EXAMPLE
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.
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.
For n=10, the numbers divisible by their last digit in base 10 are A034709 whose density is 1177/2520, therefore a(10) = 2520.
MATHEMATICA
a[n_] := Denominator[Sum[GCD[k, n]/k, {k, 1, n - 1}]/n]; Array[a, 32, 2]
CROSSREFS
Cf. A003418, A005408, A034709, A047236, A185399, A341431 (numerators).
Sequence in context: A025527 A334958 A205957 * A092144 A224497 A305753
KEYWORD
nonn,base,frac,easy
AUTHOR
Amiram Eldar, Feb 11 2021
STATUS
approved