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a(n) is the numerator of Sum_{d|n, 1 < d < n} 1/d.
1

%I #11 Jun 10 2024 10:02:46

%S 0,0,0,1,0,5,0,3,1,7,0,5,0,9,8,7,0,10,0,21,10,13,0,35,1,15,4,27,0,41,

%T 0,15,14,19,12,3,0,21,16,49,0,53,0,39,32,25,0,25,1,21,20,45,0,65,16,9,

%U 22,31,0,107,0,33,40,31,18,7,0,57,26,73,0,61,0,39,16,63,18,89,0,21

%N a(n) is the numerator of Sum_{d|n, 1 < d < n} 1/d.

%H Antti Karttunen, <a href="/A372836/b372836.txt">Table of n, a(n) for n = 1..16384</a>

%F Numerators of coefficients in expansion of Sum_{k>=2} x^(2*k) / (k * (1 - x^k)).

%e 0, 0, 0, 1/2, 0, 5/6, 0, 3/4, 1/3, 7/10, 0, 5/4, 0, 9/14, 8/15, 7/8, 0, 10/9, ...

%t nmax = 80; CoefficientList[Series[Sum[x^(2 k)/(k (1 - x^k)), {k, 2, nmax}], {x, 0, nmax}], x] // Numerator // Rest

%o (PARI) a(n) = numerator(sumdiv(n, d, if ((d>1) && (d<n), 1/d))); \\ _Michel Marcus_, May 14 2024

%Y Cf. A017665, A048050, A277790, A277791.

%K nonn,frac

%O 1,6

%A _Ilya Gutkovskiy_, May 14 2024