  We recall the notion of fractional enumeration and immediately focus on the
fractional counting of integer partitions, where each partition gets credit
equal to the reciprocal of the product of its parts. We raise two intriguing
questions regarding this count, and for each of these questions, we are
pledging a 100 US dollars donation to the OEIS in honor of the first solver. In
this revised version we announce that both questions have been answered. The
first was first answered by Will Sawin and the second was answered by
Christopher Ryba. A donation to the OEIS, of 100 US dollars each, in their
honor has been made.
