314 Jean-Marie De Koninck
49 799 889
the smallest number n such that Ω(n) = Ω(n + 1) = . . . = Ω(n + 9): here this
common value is 4 (see the number 602).
49 989 744
the smallest Niven number which is followed by at least 100 numbers (in fact
here by 107) which are not Niven numbers.
50 847 534
the number of prime numbers 109.
51 767 910
the smallest number n such that
min(λ(n), λ(n + 1), λ(n + 2), λ(n + 3), λ(n + 4), λ(n + 5))
6
5
:
here
min(λ(n), λ(n + 1), λ(n + 2), λ(n + 3), λ(n + 4), λ(n + 5))
min(1.22783, 1.40609, 1.23092, 1.62917, 1.36986, 1.27675) = 1.22783;
the next number satisfying the above inequality is n = 25 479 451 773; most
likely, there exist infinitely many numbers n satisfying the above inequality
(see the number 14 018 750, as well as J.M. De Koninck & N. Doyon [48]).
52 021 242
the 18th number n such that φ(n) + σ(n) = 3n (see the number 312).
52 521 875 (=
55
·
75)
the second number n 1 whose sum of digits is equal to
5

n (see the number
17 210 368).
53 262 468
the seventh number n such that σ3(n) is a perfect square: here σ3(53262468) =
4236745968002
(see the number 345).
56 598 313
the largest known prime number p such that
10p−1
1 (mod
p2)
(see the
number 487).
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