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A363795 Number of divisors of n of the form 7*k + 2.

%I A363795 #32 Nov 25 2023 04:28:00
%S A363795 0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,2,0,2,0,1,0,1,1,1,0,1,1,1,0,2,0,2,0,1,
%T A363795 0,2,1,1,0,1,0,1,0,2,1,2,0,2,0,1,1,1,0,2,0,1,0,2,0,2,0,1,1,2,1,1,0,1,
%U A363795 1,1,0,3,0,2,0,1,0,1,1,2,1,1,0,1,0,2,0,2,0,3,0,2,1,1,0,2,0,1,1
%N A363795 Number of divisors of n of the form 7*k + 2.
%H A363795 Amiram Eldar, <a href="/A363795/b363795.txt">Table of n, a(n) for n = 1..10000</a>
%H A363795 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 A363795 G.f.: Sum_{k>0} x^(2*k)/(1 - x^(7*k)).
%F A363795 G.f.: Sum_{k>0} x^(7*k-5)/(1 - x^(7*k-5)).
%F A363795 Sum_{k=1..n} a(k) = n*log(n)/7 + c*n + O(n^(1/3)*log(n)), where c = gamma(2,7) - (1 - gamma)/7 = 0.188117..., gamma(2,7) = -(psi(2/7) + log(7))/7 is a generalized Euler constant, and gamma is Euler's constant (A001620) (Smith and Subbarao, 1981). - _Amiram Eldar_, Nov 25 2023
%t A363795 a[n_] := DivisorSum[n, 1 &, Mod[#, 7] == 2 &]; Array[a, 100] (* _Amiram Eldar_, Jun 23 2023 *)
%o A363795 (PARI) a(n) = sumdiv(n, d, d%7==2);
%Y A363795 Cf. A279061, A363805, A363806, A363807, A363808.
%Y A363795 Cf. A001822, A001877.
%Y A363795 Cf. A284443.
%Y A363795 Cf. A001620, A016630, A354628 (psi(2/7)).
%K A363795 nonn,easy
%O A363795 1,16
%A A363795 _Seiichi Manyama_, Jun 23 2023