Those Fascinating Numbers 289
4 563 000
the fourth number n such that φ(n) + σ(n) = 4n (see the number 23 760; see
also the number 312).
4 620 799
the largest known prime number p such that P (p2 −1) 31 and P (p2 −1) = 31:
here p2 1 = 210 · 32 · 52 · 72 · 132 · 192 · 31 (see the number 4 801).
4 681 203 (= 3 · 37 · 181 · 233)
the smallest square-free composite number n such that p|n =⇒ p + 12|n + 12
(see the number 399).
4 695 456
the
12th
number n such that φ(n) + σ(n) = 3n (see the number 312).
4 713 984 (=
29
·
33
· 11 · 31)
the fifth solution of
σ(n)
n
=
10
3
(see the number 1 080).
4 729 494
the number appearing in the famous “cattle problem” of Archimedes, namely
in the Fermat-Pell equation
x2
4 729 494
y2
= 1 (see J. Stillwell [191]).
4 737 595
the fourth solution of σ2(n) = σ2(n + 10) (see the number 120).
4 989 191
the smallest number n which allows the sum
i≤n
1
i
to exceed 16 (see the number
83).
5 058 180
the fourth even number n such that σI (n) = σI (n +2) (see the number 54 178).
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