A083913 Number of divisors of n that are congruent to 3 modulo 10.

0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 1, 1

Offset

1,33

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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) - A083914(n) - A083915(n) - A083916(n) - A083917(n) - A083918(n) - A083919(n).

G.f.: Sum_{k>=1} x^(3*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(3,10) - (1 - gamma)/10 = 0.07771547..., gamma(3,10) = -(psi(3/10) + 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

a[n_] := DivisorSum[n, 1 &, Mod[#, 10] == 3 &]; Array[a, 100] (* Amiram Eldar, Dec 30 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, d % 10 == 3); \\ Amiram Eldar, Dec 30 2023

Crossrefs

Cf. A000005, A001227, A010879.

Cf. A001620, A002392, A354642 (psi(3/10)).

Cf. A083910, A083911, A083912, A083914, A083915, A083916, A083917, A083918, A083919.

Sequence in context: A351555 A215020 A103612 * A363855 A023670 A284394

Adjacent sequences: A083910 A083911 A083912 * A083914 A083915 A083916

Keyword

nonn,easy

Author

Reinhard Zumkeller, May 08 2003

Status

approved