Those Fascinating Numbers 161
4 320 (= 25 · 33 · 5)
the smallest solution of
σ(n)
n
=
7
2
; the sequence of numbers satisfying this pro-
perty begins as follows: 4 320, 4 680, 26 208, 20 427 264, 197 064 960, . . .
4 329
the third number whose square can be written as the sum of three fourth
powers: 4
3292
=
364
+
454
+
604
(see the number 481).
4 355
the smallest solution of τ (n+1)−τ (n) = 19; the sequence of numbers satisfying
this property begins as follows: 4355, 4899, 6083, 12099, 12543, 12995, 16899,
. . . (see the number 399).
4 364
the ninth solution of σ(n) = σ(n + 1) (see the number 206).
4 369
the smallest number n such that
φ12(n)
= 2, where
φ12(n)
stands for the
12th
iteration of the φ function (see the number 137).
4 374
the second number n such that P (n)
4

n and P (n + 1)
4

n + 1: here
P (4374) =√ P (2 ·
37)
= 3 8.13 . . . = 4

4374 and P (4375) = P
(54
· 7) = 7
8.13 . . . = 4 4375 (see the number 2 400).
4 418
the smallest solution of σ(n + 13) = σ(n) + 13.
4 423
the exponent of the
20th
Mersenne prime
24 423
1 (Hurwitz, 1961).
4 471
the fourth odd number k such that
2n
+ k is composite for all n k (see the
number 773): in fact,
2n
+ 4 471 is composite for all n 33 548 and prime for
n = 33 548.
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