OFFSET
1,10
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
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
a(n) = A035218(n) - ch15(n), where ch15 is the characteristic function of numbers of the form +-1 mod 6, i.e., ch15(n) = A232991(n-1).
Sum_{k=1..n} a(k) = n*log(n)/3 + c*n + O(n^(1/3)*log(n)), where c = 2*(gamma + log(12)/4 - 1)/3 = 0.132294..., and gamma is Euler's constant (A001620) (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023
MATHEMATICA
a[n_] := DivisorSum[n, 1 &, # < n && MemberQ[{1, 5}, Mod[#, 6]] &]; Array[a, 100] (* Amiram Eldar, Nov 25 2023 *)
PROG
(PARI) A320015(n) = if(!n, n, sumdiv(n, d, (d<n)&&(d%2)&&(d%3)));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Oct 03 2018
STATUS
approved