Those Fascinating Numbers 299
13 631 489
the smallest prime factor of F18 =
2218
+ 1, whose partial factorization is given
by
F18 = 13631489 · 81274690703860512587777 · C78907.
13 703 077
the third prime number p such that 23p−1 1 (mod p2) (see the number 13).
13 821 503
the smallest prime factor of the Mersenne number 2193 1, whose complete
factorization is given by
2193
1 = 13821503 · 61654440233248340616559 · 14732265321145317331353282383.
14 018 750
the smallest number n such that
min(λ(n), λ(n + 1), λ(n + 2), λ(n + 3), λ(n + 4))
5
4
:
here
min(λ(n), λ(n + 1), λ(n + 2), λ(n + 3), λ(n + 4))
(1.64261, 1.25044, 1.2668, 1.30976, 1.4742) = 1.25044;
the list of numbers satisfying the above inequality begins as follows: 14 018 750,
82 564 350, 3 387 574 069, 10 514 077 440, 11 807 429 372, 17 265 859 071,
21 036 065 792, . . . ; most likely there are infinitely many such numbers190.
14 459 929
the largest number which can be written as the sum of the seventh powers of
its digits (see the number 1 741 725).
14 520 576 (= 28 · 3 · 7 · 37 · 73)
the largest number n 109 such that
σ(n)
n
=
k
6
for some number k satisfying
(k, 6) = 1, here with k = 19 (see the number 22 932).
190Indeed,
J.M. De Koninck & N. Doyon [48] proved that, for each integer k 2, the probability
that there is only a finite number of numbers n such that
min (λ(n), λ(n + 1), . . . , λ(n + k 1))
k
k 1
is equal to zero.
Previous Page Next Page