94 Jean-Marie De Koninck
567
the smallest number n such that if A and B stand respectively for the set
of digits of n and of n2, then A B = {1, 2, 3, . . . , 9} and A B = ∅: here
5672 = 321 489; the only other number with this property is 854.
571
the smallest number n which allows the sum
m≤n
1
σ(m)
to exceed 5 (see the
number 129).
575
the smallest solution of τ (n + 1) τ (n) = 15 (see the number 399).
576
the smallest number m such that equation σ(x) = m has exactly 11 solutions,
namely 210, 282, 310, 322, 345, 357, 382, 385, 497, 517 and 527.
577
the sixth number n such that
n2
1 is powerful: here
5772
1 =
27
·
32
·
172
(see the number 485).
581
the second Canada perfect number: 52 +82 +12 = 7+83 (see the number 125).
582
the only number 1 which is equal to the sum of the squares of the factorials
of its digits in base 6: here 582 = [2, 4, 1, 0]6 = 2!2 + 4!2 + 1!2 + 0!2 (see the
number 145).
584
the ninth solution of φ(n) = φ(n + 1) (see the number 15).
586
the ninth number x such that

n≤x
λ0(n) = 0, where λ0 stands for the Liouville
function: the sequence of numbers satisfying this property begins as follows: 2,
4, 6, 10, 16, 26, 40, 96, 586, 906 150 256, . . . (see the number 906 150 256).
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