|
|
A083918
|
|
Number of divisors of n that are congruent to 8 modulo 10.
|
|
11
|
|
|
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,48
|
|
LINKS
|
|
|
FORMULA
|
Sum_{k=1..n} a(k) = n*log(n)/10 + c*n + O(n^(1/3)*log(n)), where c = gamma(8,10) - (1 - gamma)/10 = -0.176036..., gamma(8,10) = -(psi(4/5) + log(10))/10 is a generalized Euler constant, and gamma is Euler's constant (A001620) (Smith and Subbarao, 1981). - Amiram Eldar, Dec 30 2023
|
|
MATHEMATICA
|
Table[Count[Divisors[n], _?(Mod[#, 10]==8&)], {n, 110}] (* Harvey P. Dale, Sep 28 2016 *)
a[n_] := DivisorSum[n, 1 &, Mod[#, 10] == 8 &]; Array[a, 100] (* Amiram Eldar, Dec 30 2023 *)
|
|
PROG
|
(PARI) a(n) = sumdiv(n, d, d % 10 == 8); \\ Amiram Eldar, Dec 30 2023
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|