OFFSET
1,24
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
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>0} x^(3*k)/(1 - x^(7*k)).
G.f.: Sum_{k>0} x^(7*k-4)/(1 - x^(7*k-4)).
Sum_{k=1..n} a(k) = n*log(n)/7 + c*n + O(n^(1/3)*log(n)), where c = gamma(3,7) - (1 - gamma)/7 = -0.0004108181..., gamma(3,7) = -(psi(3/7) + log(7))/7 is a generalized Euler constant, and gamma is Euler's constant (A001620) (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023
MATHEMATICA
a[n_] := DivisorSum[n, 1 &, Mod[#, 7] == 3 &]; Array[a, 100] (* Amiram Eldar, Jun 23 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, d%7==3);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 23 2023
STATUS
approved