A372835 a(n) is the denominator of Sum_{d|n, d < sqrt(n)} 1/d.
1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 4, 1, 30, 1, 4, 3, 2, 5, 12, 1, 2, 3, 20, 1, 1, 1, 4, 15, 2, 1, 4, 1, 10, 3, 4, 1, 1, 5, 28, 3, 2, 1, 20, 1, 2, 21, 4, 5, 1, 1, 4, 3, 70, 1, 8, 1, 2, 15, 4, 7, 1, 1, 40
Offset: 1
Examples
0, 1, 1, 1, 1, 3/2, 1, 3/2, 1, 3/2, 1, 11/6, 1, 3/2, 4/3, 3/2, 1, 11/6, ...
Programs
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Mathematica
nmax = 80; CoefficientList[Series[Sum[x^(k (k + 1))/(k (1 - x^k)), {k, 1, nmax}], {x, 0, nmax}], x] // Denominator // Rest -
PARI
a(n) = denominator(sumdiv(n, d, if (d^2 < n, 1/d))); \\ Michel Marcus, May 14 2024
Formula
Denominators of coefficients in expansion of Sum_{k>=1} x^(k*(k+1)) / (k * (1 - x^k)).