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A341431
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a(n) is the numerator of the asymptotic density of numbers divisible by their last digit in base n.
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4
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1, 1, 7, 5, 37, 7, 421, 347, 1177, 671, 14939, 6617, 135451, 140311, 271681, 143327, 5096503, 751279, 91610357, 24080311, 9098461, 830139, 2188298491, 77709491, 925316723, 6609819823, 3567606143, 10876020307, 123417992791, 300151059037, 37903472946337, 32271030591223
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OFFSET
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2,3
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LINKS
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FORMULA
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EXAMPLE
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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, ...
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.
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.
For n=10, the numbers divisible by their last digit in base 10 are A034709 whose density is 1177/2520, therefore a(10) = 1177.
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MATHEMATICA
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a[n_] := Numerator[Sum[GCD[k, n]/k, {k, 1, n - 1}]/n]; Array[a, 32, 2]
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CROSSREFS
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KEYWORD
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nonn,base,frac,easy
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AUTHOR
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STATUS
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approved
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