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

%I A293898 #15 Nov 27 2023 03:04:28
%S A293898 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,
%T A293898 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,
%U A293898 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
%N A293898 Sum of proper divisors of n of the form 3k+2.
%H A293898 Antti Karttunen, <a href="/A293898/b293898.txt">Table of n, a(n) for n = 1..20000</a>
%H A293898 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>.
%F A293898 a(n) = A078182(n) - ([n == 2 (mod 3)]*n).
%F A293898 G.f.: Sum_{k>=1} (3*k-1) * x^(6*k-2) / (1 - x^(3*k-1)). - _Ilya Gutkovskiy_, Apr 14 2021
%F A293898 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
%t A293898 Table[DivisorSum[n, # &, And[Mod[#, 3] == 2, # != n] &], {n, 105}] (* _Michael De Vlieger_, Nov 08 2017 *)
%o A293898 (PARI) A293898(n) = sumdiv(n,d,(d<n)*(2==(d%3))*d);
%Y A293898 Cf. A078182, A293896, A293897.
%K A293898 nonn,easy
%O A293898 1,4
%A A293898 _Antti Karttunen_, Nov 06 2017