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%I #7 May 18 2024 15:08:18
%S 1,1,1,3,1,3,1,3,4,3,1,11,1,3,4,7,1,11,1,7,4,3,1,25,6,3,4,7,1,61,1,7,
%T 4,3,6,9,1,3,4,39,1,2,1,7,23,3,1,9,8,17,4,7,1,2,6,53,4,3,1,49,1,3,31,
%U 15,6,2,1,7,4,129,1,19,1,3,23,7,8,2,1,83
%N a(n) is the numerator of Sum_{d|n, d <= sqrt(n)} 1/d.
%F Numerators of coefficients in expansion of Sum_{k>=1} x^(k^2) / (k * (1 - x^k)).
%e 1, 1, 1, 3/2, 1, 3/2, 1, 3/2, 4/3, 3/2, 1, 11/6, 1, 3/2, 4/3, 7/4, 1, 11/6, ...
%t nmax = 80; CoefficientList[Series[Sum[x^(k^2)/(k (1 - x^k)), {k, 1, nmax}], {x, 0, nmax}], x] // Numerator // Rest
%o (PARI) a(n) = numerator(sumdiv(n, d, if (d^2 <= n, 1/d))); \\ _Michel Marcus_, May 14 2024
%Y Cf. A017665, A066839, A372833 (denominators).
%K nonn,frac
%O 1,4
%A _Ilya Gutkovskiy_, May 14 2024
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