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A363897 Expansion of Sum_{k>0} k * x^k / (1 - x^(5*k)).

%I A363897 #18 Jun 29 2023 11:50:29
%S A363897 1,2,3,4,5,7,7,8,9,10,12,14,13,14,15,17,17,21,19,20,22,24,23,28,25,27,
%T A363897 27,28,29,35,32,34,36,34,35,43,37,38,39,40,42,51,43,48,45,47,47,59,49,
%U A363897 50,52,54,53,63,60,57,57,58,59,70,62,64,66,68,65,84,67,68,69,70,72,86,73,74,75,77,84,94
%N A363897 Expansion of Sum_{k>0} k * x^k / (1 - x^(5*k)).
%H A363897 Seiichi Manyama, <a href="/A363897/b363897.txt">Table of n, a(n) for n = 1..10000</a>
%F A363897 a(n) = Sum_{d|n, n/d==1 mod 5} d.
%F A363897 G.f.: Sum_{k>0} x^(5*k-4) / (1 - x^(5*k-4))^2.
%t A363897 a[n_] := DivisorSum[n, # &, Mod[n/#, 5] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Jun 27 2023 *)
%o A363897 (PARI) a(n) = sumdiv(n, d, (n/d%5==1)*d);
%Y A363897 Cf. A363898, A363899, A363900.
%Y A363897 Cf. A002131, A050460, A326399.
%Y A363897 Cf. A001876, A284097.
%K A363897 nonn
%O A363897 1,2
%A A363897 _Seiichi Manyama_, Jun 27 2023