Those Fascinating Numbers 203
22 480
the sixth and largest solution y of the diophantine equation
x2
+ 999 =
y3
(see
the number 251).
22 624
the smallest number n such that each of the numbers n+i, 0 i 3, is divisible
by a cube 1: 22 624 = 25 · 7 · 101, 22 625 = 53 · 181, 22 626 = 2 · 33 · 419,
22 627 =
113
· 17 (see the number 242).
22 736
the largest number n such that the corresponding triangular number Tn =
n(n+1)
2
is the product of three consecutive numbers: here
22 736 · 22 737
2
= 636 · 637 · 638
(see the number 608).
22 865
the seventh number which is not a palindrome, but whose square is a palindrome
(see the number 26).
22 932
the second number n such that
σ(n)
n
=
k
6
for some k satisfying (k, 6) = 1, here
with k = 19; the only solutions n
109
of this equation are 18, 22 932 and
14 520 576.
22 971
the
22nd
number n such that n ·
2n
1 is prime (see the number 115).
23 005
the 23rd number n such that n · 2n 1 is prime (see the number 115).
23 209
the exponent of the
26th
Mersenne prime
223 209
1 (Noll, 1979).
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