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A188170
The number of divisors d of n of the form d == 3 (mod 8).
10
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 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
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Mar 23 2011
STATUS
approved