A293901 Sum of proper divisors of n of the form 4k+1.

0, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 10, 1, 6, 1, 1, 1, 1, 6, 14, 10, 1, 1, 6, 1, 1, 1, 18, 6, 10, 1, 1, 14, 6, 1, 22, 1, 1, 15, 1, 1, 1, 1, 31, 18, 14, 1, 10, 6, 1, 1, 30, 1, 6, 1, 1, 31, 1, 19, 34, 1, 18, 1, 6, 1, 10, 1, 38, 31, 1, 1, 14, 1, 6, 10, 42, 1, 22, 23, 1, 30, 1, 1, 60, 14, 1, 1, 1, 6, 1, 1, 50, 43, 31, 1, 18, 1, 14, 27

Offset

1,10

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to sums of divisors.

Formula

a(n) = Sum_{d|n, d<n} [1 == d mod 4]*d.

a(n) = A091570(n) - A293903(n).

G.f.: Sum_{k>=1} (4*k-3) * x^(8*k-6) / (1 - x^(4*k-3)). - 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

a[n_] := DivisorSum[n, # &, # < n && Mod[#, 4] == 1 &]; Array[a, 100] (* Amiram Eldar, Nov 27 2023 *)

Prog

(PARI) A293901(n) = sumdiv(n, d, (d<n)*(1==(d%4))*d);

Crossrefs

Cf. A050449, A091570, A293451, A293903.

Sequence in context: A268731 A080219 A339747 * A324891 A260340 A040037

Adjacent sequences: A293898 A293899 A293900 * A293902 A293903 A293904

Keyword

nonn,easy

Author

Antti Karttunen, Oct 19 2017

Status

approved