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
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
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Mar 23 2011
STATUS
approved