166 Jean-Marie De Koninck
5 187
the
17th
solution of φ(n) = φ(n + 1) (see the number 15).
5 234
the largest solution y of the diophantine equation x2 17 = y3: T. Nagel
[147] proved that this diophantine equation has exactly 16 solutions (x, y),
namely the solutions (±3, −2), (±4, −1), (±5, 2), (±9, 4), (±23, 8), (±282, 43),
(±375, 52), (±378661, 5234) (see also Sierpinski [185], p.104).
5 264
the smallest number n such that n and n+1 each have six prime factors counting
their multiplicity: 5 264 =
24
· 7 · 47 and 5 265 =
34
· 5 · 13 (see the number 135).
5 312
the 16th number n such that n · 2n 1 is prime (see the number 115);
the second number n such that Eφ(n) := φ(n + 1) φ(n) satisfies Eφ(n + 1) =
Eφ(n): here the common value of is 16, since φ(5 312) = 2 624, φ(5 313) =
2 640 and φ(5 314) = 2 656; the sequence of numbers satisfying this property
begins as follows: 5 186, 5 312, 273 524, . . .
5 337
the sixth composite number n such that σ(n + 6) = σ(n) + 6 (see the number
104).
5 346 (= 2 · 35 · 11)
the fourth number n having at least two distinct prime factors and such that
B1(n) = β(n)2: here 2 + 35 + 11 = (2 + 3 + 11)2 (see the number 144).
5 355
the eighth odd abundant number (see the number 945).
5 361
the number of integer zeros of the function M(x) :=
n≤x
µ(n) located in the
interval [1,
106]
(see the number 92).
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