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A293513
Number of proper divisors of n of the form 4k+3.
3
0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 1, 1, 0, 1, 1, 0, 0, 2, 0, 1, 2, 1, 0, 1, 1, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0, 2, 2, 0, 1, 0, 0, 2, 1, 2, 2, 0, 0, 2, 0, 0, 2, 0, 1, 1, 1, 0, 2, 1, 1, 2, 1, 1, 1, 0, 1, 2, 0, 0, 2, 0, 0, 4
OFFSET
1,21
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
a(n) = Sum_{d|n, d<n} [3 == d mod 4].
a(n) = A091954(n) - A293451(n).
a(n) = A001842(n) - A121262(n+1).
G.f.: Sum_{k>=1} x^(8*k-2) / (1 - x^(4*k-1)). - Ilya Gutkovskiy, Apr 14 2021
Sum_{k=1..n} a(k) = n*log(n)/4 + c*n + O(n^(1/3)*log(n)), where c = gamma(3,4) - (2 - gamma)/4 = A256846 - (2 - A001620)/4 = -0.430804... (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023
MATHEMATICA
a[n_] := DivisorSum[n, 1 &, # < n && Mod[#, 4] == 3 &]; Array[a, 100] (* Amiram Eldar, Nov 25 2023 *)
PROG
(PARI) A293513(n) = sumdiv(n, d, (d<n)*(3==(d%4)));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Oct 19 2017
STATUS
approved