• Leate_Wonceslace@lemmy.dbzer0.com
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    5 months ago

    31521281 = 11 × 17 × 59 × 2857

    11 × 17 = 187

    11 × 59 = 649

    11 × 2857 = 31427

    17 × 59 = 10003

    17 × 2857 = 48569

    59 × 2857 = 168563

    17 × 59 × 2857 = 2865571

    11 × 59 × 2857 = 1854193

    11 × 17 × 2857 = 534259

    11 × 17 × 59 = 11033

    11+17+59+2857+11033+534259+1854193+2865571+168563+ 48569+10003+31427+649+187=5527398≠31521281

    • Arthur Besse@lemmy.ml
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      5 months ago

      17 × 59 = 10003

      you’ve got an extra zero in there, and you forgot the 1, but the rest of your divisors match my crude brute-force approach:

      >>> n=31521281
      >>> d = [ x for x in range(1,n//2+1) if not n%x ]
      >>> d
      [1, 11, 17, 59, 187, 649, 1003, 2857, 11033, 31427, 48569, 168563, 534259, 1854193, 2865571]
      >>> yours=list(map(int,"11+17+59+2857+11033+534259+1854193+2865571+168563+48569+10003+31427+649+187".split("+")))
      >>> set(yours) - set(d)
      {10003}
      >>> set(d) - set(yours)
      {1, 1003}
      >>> sum(d)
      5518399
      

      same conclusion though: 5518399 also ≠ 31521281

      bonus nonsense
      >>> isperfect = lambda n: n == sum(x for x in range(1,n//2+1) if not n%x)
      >>> [n for n in range(1, 10000) if isperfect(n)]
      [6, 28, 496, 8128]
      

      (from https://oeis.org/A000396 i see the next perfect number after 8128 is 33550336 which is too big for me to wait for the naive approach above to test…)

      more bonus nonsense
      >>> divisors_if_perfect = lambda n: n == sum(d:=[x for x in range(1,n//2+1) if not n%x]) and d
      >>> print("\n".join(f"{n:>5} == sum{tuple(d)}" for n in range(10000) if (d:=divisors_if_perfect(n))))
          6 == sum(1, 2, 3)
         28 == sum(1, 2, 4, 7, 14)
        496 == sum(1, 2, 4, 8, 16, 31, 62, 124, 248)
       8128 == sum(1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064)