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A293903
Sum of proper divisors of n of the form 4k+3.
3
0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 7, 3, 0, 0, 3, 0, 0, 10, 11, 0, 3, 0, 0, 3, 7, 0, 18, 0, 0, 14, 0, 7, 3, 0, 19, 3, 0, 0, 10, 0, 11, 18, 23, 0, 3, 7, 0, 3, 0, 0, 30, 11, 7, 22, 0, 0, 18, 0, 31, 10, 0, 0, 14, 0, 0, 26, 42, 0, 3, 0, 0, 18, 19, 18, 42, 0, 0, 30, 0, 0, 10, 0, 43, 3, 11, 0, 18, 7, 23, 34, 47, 19, 3, 0, 7, 14, 0, 0, 54, 0, 0, 60
OFFSET
1,6
FORMULA
a(n) = Sum_{d|n, d<n} [3 == d mod 4]*d.
a(n) = A091570(n) - A293901(n).
G.f.: Sum_{k>=1} (4*k-1) * x^(8*k-2) / (1 - x^(4*k-1)). - Ilya Gutkovskiy, Apr 14 2021
Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/48 - 1/8 = 0.0806167... . - Amiram Eldar, Nov 27 2023
MATHEMATICA
Array[DivisorSum[#, # &, Mod[#, 4] == 3 &] - Boole[Mod[#, 4] == 3] # &, 105] (* Michael De Vlieger, Oct 23 2017 *)
PROG
(PARI) A293903(n) = sumdiv(n, d, (d<n)*(3==(d%4))*d);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Oct 19 2017
STATUS
approved