OFFSET
1,12
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) = A000005(n) - A083910(n) - A083911(n) - A083913(n) - A083914(n) - A083915(n) - A083916(n) - A083917(n) - A083918(n) - A083919(n).
G.f.: Sum_{k>=1} x^(2*k)/(1 - x^(10*k)). - Ilya Gutkovskiy, Sep 11 2019
Sum_{k=1..n} a(k) = n*log(n)/10 + c*n + O(n^(1/3)*log(n)), where c = gamma(2,10) - (1 - gamma)/10 = 0.256367..., gamma(2,10) = -(psi(1/5) + log(10))/10 is a generalized Euler constant, and gamma is Euler's constant (A001620) (Smith and Subbarao, 1981). - Amiram Eldar, Dec 30 2023
MATHEMATICA
a[n_] := Sum[If[Mod[d, 10] == 2, 1, 0], {d, Divisors[n]}];
Array[a, 105] (* Jean-François Alcover, Dec 02 2021 *)
a[n_] := DivisorSum[n, 1 &, Mod[#, 10] == 2 &]; Array[a, 100] (* Amiram Eldar, Dec 30 2023 *)
PROG
(PARI) A083912(n) = sumdiv(n, d, 2==(d%10)); \\ Antti Karttunen, Jan 22 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, May 08 2003
STATUS
approved