A363808 Number of divisors of n of the form 7*k + 6.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0

Offset

1,48

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^(6*k)/(1 - x^(7*k)).

G.f.: Sum_{k>0} x^(7*k-1)/(1 - x^(7*k-1)).

Sum_{k=1..n} a(k) = n*log(n)/7 + c*n + O(n^(1/3)*log(n)), where c = gamma(6,7) - (1 - gamma)/7 = -0.218328..., gamma(6,7) = -(psi(6/7) + 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] == 6 &]; Array[a, 100] (* Amiram Eldar, Jun 23 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, d%7==6);

Crossrefs

Cf. A279061, A363795, A363805, A363806, A363807.

Cf. A284105.

Cf. A001620, A016630, A354632 (psi(6/7)).

Sequence in context: A336107 A350251 A367783 * A227761 A037188 A276847

Adjacent sequences: A363805 A363806 A363807 * A363809 A363810 A363811

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 23 2023

Status

approved