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A363807
Number of divisors of n of the form 7*k + 5.
11
0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 2, 0, 0, 1, 1
OFFSET
1,40
LINKS
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^(5*k)/(1 - x^(7*k)).
G.f.: Sum_{k>0} x^(7*k-2)/(1 - x^(7*k-2)).
Sum_{k=1..n} a(k) = n*log(n)/7 + c*n + O(n^(1/3)*log(n)), where c = gamma(5,7) - (1 - gamma)/7 = -0.169787..., gamma(5,7) = -(psi(5/7) + 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] == 5 &]; Array[a, 100] (* Amiram Eldar, Jun 23 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, d%7==5);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 23 2023
STATUS
approved