Those Fascinating Numbers 267
673 663
the third composite number n such that 2n−4 1 (mod n); see the number
40 369.
675 214
the smallest number n which allows the sum
i≤n
1
i
to exceed 14 (see the num-
ber 83).
678 570
the
11th
Bell number (see the number 52).
703 125
the smallest number whose index of composition is 4 and which can be
written as the sum of two co-prime numbers each with an index of composition
3: indeed,
703 125 = 2 197 + 700 928,
32
·
57
=
133
+
29
·
372,
with
λ(32
·
57)
4.97158,
λ(133)
= 3 and
λ(29
·
372)
3.12731; the sequence of
numbers satisfying this property begins as follows: 703 125, 720 896, 3 418 801,
6 815 744, . . . 185
706 063
the eighth number n such that φ(n)σ(n) is a fourth power: here
φ(706063)σ(706063) = 8404 (see the number 170).
706 237
the ninth number n such that φ(n)σ(n) is a fourth power: here
φ(706237)σ(706237) = 8404 (see the number 170).
709 838
the fifth number n such that

p≤pn
p is a perfect square: here we have

p≤p709838
p =
19163572
(see the number 2 474).
185One
can easily show that if the abc Conjecture is true, then there is only a finite number of
numbers with this property.
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