  More than 70 years ago it was recognised that ionospheric F2-layer critical
frequencies $foF2$ had a strong relationship to sunspot number. Using historic
datasets from the Slough and Washington ionosondes, we evaluate the best
statistical fits of $foF2$ to sunspot numbers (at each Universal Time [UT]
separately) in order to search for drifts and abrupt changes in the fit
residuals over Solar Cycles 17 - 21. Polynomial fits are made both with and
without allowance for the white-light facular area, which has been reported as
being associated with cycle-to-cycle changes in the sunspot number - $foF2$
relationship. Over the interval studied here, the ISN, $R$, the backbone group
number $Rbb$, and the corrected number $Rc$ largely differ in their allowance
for the 'Waldmeier discontinuity' around 1945 (the correction factor for which
for $R$, $Rbb$ and $Rc$ is, respectively, zero, effectively over 20%, and
explicitly 11.6%). It is shown that for Solar Cycles 18 - 21, all three sunspot
data sequences perform well, but that the fit residuals are lowest and most
uniform for $Rbb$. We here use $foF2$ for those UTs for which $R$, $Rbb$, and
$Rc$ all give correlations exceeding 0.99 for intervals both before and after
the Waldmeier discontinuity. The error introduced by the Waldmeier
discontinuity causes $R$ to underestimate the fitted values based on the $foF2$
data for 1932 - 1945 but $Rbb$ overestimates them by almost the same factor,
implying that the correction for the Waldmeier discontinuity inherent in $Rbb$
is too large by a factor of two. Fit residuals are smallest and most uniform
for $Rc$ and the ionospheric data support the optimum discontinuity
multiplicative correction factor derived from the independent Royal Greenwich
Observatory (RGO) sunspot group data for the same interval.
