A188170 The number of divisors d of n of the form d == 3 (mod 8).

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

Offset

1,27

Comments

a(3n) >= 1 as the divisor d=3 contributes to the count then.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael D. Hirschhorn, The number of representations of a number by various forms, Discrete Mathematics 298 (2005), 205-211.

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) + A188172(n) = A001842(n).

A188169(n) + a(n) - A188171(n) - A188172(n) = A002325(n).

G.f.: Sum_{k>=1} x^(3*k)/(1 - x^(8*k)). - Ilya Gutkovskiy, Sep 11 2019

Sum_{k=1..n} a(k) = n*log(n)/8 + c*n + O(n^(1/3)*log(n)), where c = gamma(3,8) - (1 - gamma)/8 = A256782 - (1 - A001620)/8 = 0.0314716... (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023

Maple

sigmamr := proc(n, m, r) local a, d ; a := 0 ; for d in numtheory[divisors](n) do if modp(d, m) = r then a := a+1 ; end if; end do: a; end proc:
A188170 := proc(n) sigmamr(n, 8, 3) ; end proc:

Mathematica

Table[Count[Divisors[n], _?(Mod[#, 8]==3&)], {n, 100}] (* Harvey P. Dale, Jul 08 2013 *)

Prog

(PARI) a(n) = sumdiv(n, d, (d%8) == 3); \\ Michel Marcus, Nov 05 2018

Crossrefs

Cf. A001842, A002325, A188169, A188171, A188172.

Cf. A001620, A256782.

Sequence in context: A363855 A023670 A284394 * A363805 A212193 A253189

Adjacent sequences: A188167 A188168 A188169 * A188171 A188172 A188173

Keyword

nonn,easy

Author

R. J. Mathar, Mar 23 2011

Status

approved