214 Jean-Marie De Koninck
39 999
the smallest solution of τ (n + 1) τ (n) = 27 (see the number 399).
40 001
the third composite number of the form k · 10k + 1 (see the number 201).
40 311
the eighth number n such that n, n + 1, n + 2, n + 3 and n + 4 have the same
number of divisors, namely eight (see the number 11 605).
40 320
the value of 8! .
40 369
the second composite number n such that 2n−4 1 (mod n); the only com-
posite numbers n 108 satisfying this property are 4, 40 369, 673 663, 990 409,
1 697 609, 2 073 127, 6 462 649, 7 527 199, 7 559 479, 14 421 169, 21 484 129,
37 825 753 and 57 233 047.
40 391
the sixth solution w of the aligned houses problem (see the number 35).
40 465
the smallest number which is equal to the sum of the factorials of its digits in
base 17: here 40 465 = [8, 4, 0, 5]17 = 8! + 4! + 0! + 5! (see the numbers 145 and
40 472).
40 472
the largest number which is equal to the sum of the factorials of its digits in
base 11: here 40 472 = [2, 8, 4, 5, 3]11 = 2! + 8! + 4! + 5! + 3!; the only numbers
with this property are 1, 2, 26, 48 and 40 472 (see also the number 145).
40 487
the third odd prime number p such that
5p−1
1 (mod
p2)
(see the number
20 771);
the smallest prime number p whose smallest primitive root modulo p (namely
here 5) is not a primitive root modulo
p2
(a problem stated by Neville Rob-
bins at the 1998 West Coast Number Theory Conference and solved by many
participants).
Previous Page Next Page