184 Jean-Marie De Koninck
10 343
the prime number which appears the most often as the
16th
prime factor of an
integer (see the number 199).
10 368
the smallest number n = [d1, d2, . . . , dr] such that (d1 +r)·(d2 +r −1)·. . .·(dr +
1) = n; the set of numbers satisfying this property is finite and its members
are 10 368, 34 496, 9 317 179 872, 2 974 959 187 200 and 3 942 878 404 608 000;
the fifth number n which is equal to the product of the factorials of its digits
in base 5: 10 368 = [3, 1, 2, 4, 3, 3]5 = 3! · 1! · 2! · 4! · 3! · 3! (see the number 144).
10 370
the smallest number n which can be written as the sum of the squares of two
prime numbers in four distinct ways: 10 370 =
132
+
1012
=
312
+
972
=
592
+
832
=
712
+
732
(see the number 338).
10 430
the eighth bizarre number (see the number 70).
10 529
the smallest prime number p such that Ω(p 1) = Ω(p + 1) = 7: here 10 528 =
25
· 7 · 47 and 10 530 = 2 ·
34
· 5 · 13 (see the number 271).
10 537
the smallest number n such that
φ13(n)
= 2, where
φ13(n)
stands for the
13th
iteration of the φ function (see the number 137).
10 585
the eighth Carmichael number (see the number 561).
10 604
the
18th
solution of φ(n) = φ(n + 1) (see the number 15).
10 691
the
33rd
Lucas prime number (see the number 613).
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