A083918 Number of divisors of n that are congruent to 8 modulo 10.

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

Offset

1,48

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

R. A. Smith and M. V. Subbarao, The average number of divisors in an arithmetic progression, Canadian Mathematical Bulletin, Vol. 24, No. 1 (1981), pp. 37-41.

Formula

a(n) = A000005(n) - A083910(n) - A083911(n) - A083912(n) - A083913(n) - A083914(n) - A083915(n) - A083916(n) - A083917(n) - A083919(n).

G.f.: Sum_{k>=1} x^(8*k)/(1 - x^(10*k)). - Ilya Gutkovskiy, Sep 11 2019

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

Cf. A000005, A001227, A010879.

Cf. A001620, A002392, A200138 (psi(4/5)).

Cf. A083910, A083911, A083912, A083913, A083914, A083915, A083916, A083917, A083919.

Sequence in context: A368843 A127268 A252459 * A083895 A093488 A085858

Adjacent sequences: A083915 A083916 A083917 * A083919 A083920 A083921

Keyword

nonn,easy

Author

Reinhard Zumkeller, May 08 2003

Status

approved