302 Jean-Marie De Koninck
17 907 119
the smallest number n satisfying φ(n) = 5φ(n + 1); the sequence of num-
bers satisfying this property begins as follows: 17907119, 18828809, 31692569,
73421039, 179467469, . . . (see the number 629).
18 003 384 (= 23 · 38 · 73)
the fifth number n having at least two distinct prime factors and such that
β(n)3|B1(n): here (2 + 3 + 7)3|(23 + 38 + 73) (see the number 5 120).
18 035 622
the smallest of the first four consecutive numbers being each divisible by a
cube 1: 18 035 622 = 2 ·
34
· 11 · 29 · 349, 18 035 623 =
173
· 3671, 18 035 624 =
23
· 163 · 13831, 18 035 625 = 3 ·
54
· 9619 and 18 035 626 = 2 ·
73
· 61 · 431 (see
the number 844).
18 506 880 (=
27
·
35
· 5 · 7 · 17)
the smallest solution of
σ(n)
n
=
13
3
: the only solutions n 109 of this equation
are 18 506 880, 36 197 280 and 299 980 800.
18 673 201
the second number n such that φ(n + 1) = 5φ(n) (see the number 11 242 770).
19 099 919
the smallest prime number q1 such that each number qi = 2qi−1 + 1 is prime
for i = 2, 3, . . . , 8: such a sequence of prime numbers is called a Cunningham
chain (see the number 1 122 659).
19 592 147
the fourth number which can be written in two distinct ways as the sum of
two co-prime numbers each with an index of composition 5: 19 592 147 =
313
+
213
·
133
=
24
·
38
+
117,
these last four numbers having as index of
composition 13, 5.12746, 6.45259 and 7 respectively (see the number 371 549).
19 720 007
the ninth solution of σ2(n) = σ2(n + 2) (see the number 1 079).
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