• Leate_Wonceslace@lemmy.dbzer0.com
      link
      fedilink
      English
      arrow-up
      9
      ·
      edit-2
      6 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
        link
        fedilink
        English
        arrow-up
        6
        ·
        edit-2
        6 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)