A293903 Sum of proper divisors of n of the form 4k+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

Author

Antti Karttunen, Oct 19 2017

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to sums of divisors.

Crossrefs

Cf. A050452, A091570, A293513, A293901.

Programs

Mathematica

Array[DivisorSum[#, # &, Mod[#, 4] == 3 &] - Boole[Mod[#, 4] == 3] # &, 105] (* Michael De Vlieger, Oct 23 2017 *)

PARI

A293903(n) = sumdiv(n,d,(d
				

Formula

a(n) = Sum_{d|n, 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

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