Those Fascinating Numbers 167
5 395
the third solution of σ2(n) = σ2(n + 10) (see the number 120).
5 407
the sixth prime number q such that

p≤q
p is a multiple of 100: here this sum
is equal to 1 776 800 (see the number 563).
5 472
the second dihedral 3-perfect number n, that is such that τ (n)+ σ(n) = 3n: the
only three numbers n 109 satisfying this property are 60, 5 472 and 2 500 704.
5 525 (=
52
· 13 · 17)
the smallest number which can be written as the sum of two squares in five
distinct ways (as well as six distinct ways), namely 5 525 =
72
+
742
=
142
+
732
=
222
+
712
=
252
+
702
=
412
+
602
=
502
+
552
(see the number 50).
5 569
the largest known150 prime number p for which there exists an even number
n (namely here n = 389 965 026 819 938) such that n q is composite for each
prime number q p (see J. Richstein [171]): here we have the “Goldbach
representation” 389 965 026 819 938 = 5 569 + 389 965 026 814 369.
5 597
the number of pseudoprimes in base 2 smaller than
109
(see the number 245).
5 694
the smallest number n such that βI (n) = βI (n+1) = βI (n+2), where βI (n) :=

p|n,p2
p: here 5 694 = 2 · 3 · 13 · 73, 5 695 = 5 · 17 · 67 and 5 696 =
26
· 89, while
the common value of βI (n + i) is 89; the second number with this property is
2 463 803 977 (see also the number 89 460 294).
5 719
the sixth Lucas-Carmichael number(see the number 399).
150It is possible to prove that there exist infinitely many prime numbers p satisfying this property.
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