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A341431 a(n) is the numerator of the asymptotic density of numbers divisible by their last digit in base n. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

LINKS

Amiram Eldar, Table of n, a(n) for n = 2..2300

FORMULA

a(n)/A341432(n) = Sum_{k=1..n-1} gcd(k, n)/k.

EXAMPLE

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.

MATHEMATICA

a[n_] := Numerator[Sum[GCD[k, n]/k, {k, 1, n - 1}]/n]; Array[a, 32, 2]

CROSSREFS

Cf. A005408, A034709, A047236, A341432 (denominators).

Sequence in context: A344917 A328758 A070426 * A142883 A146382 A163742

Adjacent sequences:  A341428 A341429 A341430 * A341432 A341433 A341434

KEYWORD

nonn,base,frac,easy

AUTHOR

Amiram Eldar, Feb 11 2021

STATUS

approved

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Last modified December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)