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A001878 Number of divisors of n of the form 5k+3; a(0) = 0.

%I A001878 #25 Nov 25 2023 04:35:23
%S A001878 0,0,0,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0,2,0,0,1,0,1,2,0,1,1,1,0,1,0,1,2,
%T A001878 0,0,2,0,1,2,1,0,1,1,0,1,1,0,3,0,0,1,1,1,2,0,2,1,1,0,1,0,0,2,1,1,2,0,
%U A001878 1,2,0,0,3,1,0,1,1,0,3,0,1,1,0,1,2,0,1,1
%N A001878 Number of divisors of n of the form 5k+3; a(0) = 0.
%H A001878 T. D. Noe, <a href="/A001878/b001878.txt">Table of n, a(n) for n = 0..10000</a>
%H A001878 R. A. Smith and M. V. Subbarao, <a href="https://doi.org/10.4153/CMB-1981-005-3">The average number of divisors in an arithmetic progression</a>, Canadian Mathematical Bulletin, Vol. 24, No. 1 (1981), pp. 37-41.
%F A001878 G.f.: Sum_{n>=0} x^(5*n+3)/(1 - x^(5*n+3)).
%F A001878 G.f.: Sum_{k>=1} x^(3*k)/(1 - x^(5*k)). - _Ilya Gutkovskiy_, Sep 11 2019
%F A001878 Sum_{k=1..n} a(k) = n*log(n)/5 + c*n + O(n^(1/3)*log(n)), where c = gamma(3,5) - (1 - gamma)/5 = A256848 - (1 - A001620)/5 = -0.0983206... (Smith and Subbarao, 1981). - _Amiram Eldar_, Nov 25 2023
%t A001878 Join[{0}, Table[d = Divisors[n]; Length[Select[d, Mod[#, 5] == 3 &]], {n, 100}]] (* _T. D. Noe_, Aug 10 2012 *)
%t A001878 Table[Count[Divisors[n],_?(Mod[#,5]==3&)],{n,0,90}] (* _Harvey P. Dale_, Nov 08 2012 *)
%o A001878 (PARI) a(n) = if (n==0, 0, sumdiv(n, d, (d % 5)==3)); \\ _Michel Marcus_, Feb 28 2021
%Y A001878 Cf. A001876, A001877, A001899.
%Y A001878 Cf. A001620, A256848.
%K A001878 nonn,easy
%O A001878 0,19
%A A001878 _N. J. A. Sloane_