A083914 Number of divisors of n that are congruent to 4 modulo 10.

0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0

Offset

1,24

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Antti Karttunen, Data supplement: n, a(n) computed for n =  1..100000

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

G.f.: Sum_{k>=1} x^(4*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(4,10) - (1 - gamma)/10 = -0.0163984..., gamma(4,10) = -(psi(2/5) + 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]==4&)], {n, 110}] (* Harvey P. Dale, Dec 09 2014 *)
a[n_] := DivisorSum[n, 1 &, Mod[#, 10] == 4 &]; Array[a, 100] (* Amiram Eldar, Dec 30 2023 *)

Prog

(PARI) A083914(n) = sumdiv(n, d, (4==(d%10))); \\ Antti Karttunen, Nov 07 2018

Crossrefs

Cf. A000005, A001227, A010879.

Cf. A001620, A002392, A200136 (psi(2/5)).

Cf. A083910, A083911, A083912, A083913, A083915, A083916, A083917, A083918, A083919.

Sequence in context: A130207 A325433 A167688 * A083891 A363860 A087623

Adjacent sequences: A083911 A083912 A083913 * A083915 A083916 A083917

Keyword

nonn,easy

Author

Reinhard Zumkeller, May 08 2003

Status

approved