A293898 Sum of proper divisors of n of the form 3k+2.

0, 0, 0, 2, 0, 2, 0, 2, 0, 7, 0, 2, 0, 2, 5, 10, 0, 2, 0, 7, 0, 13, 0, 10, 5, 2, 0, 16, 0, 7, 0, 10, 11, 19, 5, 2, 0, 2, 0, 35, 0, 16, 0, 13, 5, 25, 0, 10, 0, 7, 17, 28, 0, 2, 16, 24, 0, 31, 0, 27, 0, 2, 0, 42, 5, 13, 0, 19, 23, 56, 0, 10, 0, 2, 5, 40, 11, 28, 0, 35, 0, 43, 0, 16, 22, 2, 29, 65, 0, 7, 0, 25, 0, 49, 5, 42, 0, 16, 11, 77, 0, 19, 0, 36, 40

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sums of divisors.

Formula

a(n) = A078182(n) - ([n == 2 (mod 3)]*n).

G.f.: Sum_{k>=1} (3*k-1) * x^(6*k-2) / (1 - x^(3*k-1)). - Ilya Gutkovskiy, Apr 14 2021

Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/36 - 1/6 = 0.107489... . - Amiram Eldar, Nov 27 2023

Mathematica

Table[DivisorSum[n, # &, And[Mod[#, 3] == 2, # != n] &], {n, 105}] (* Michael De Vlieger, Nov 08 2017 *)

Prog

(PARI) A293898(n) = sumdiv(n, d, (d<n)*(2==(d%3))*d);

Crossrefs

Cf. A078182, A293896, A293897.

Sequence in context: A333808 A307692 A300548 * A368817 A324301 A361235

Adjacent sequences: A293895 A293896 A293897 * A293899 A293900 A293901

Keyword

nonn,easy

Author

Antti Karttunen, Nov 06 2017

Status

approved