Those Fascinating Numbers 337
919 501 200
the 11th number n such that φ(n) + σ(n) = 4n (see the number 23 760).
965 009 045
the smallest number n such that ω(n) = ω(n + 1) = 7; in fact, 965 009 045 =
5 · 7 · 11 · 13 · 23 · 83 · 101 and 965 009 046 = 2 · 3 · 17 · 29 · 41 · 73 · 109 (see the
number 230).
987 654 103
the largest prime number made up of exactly nine distinct digits (see the num-
ber 9 871).
987 654 321
the only nine digit self replicating number (see the number 954).
999 979 163
the smallest number which can be written as the sum of the cubes of three
distinct prime numbers in four distinct ways:
999 979 163 =
833
+
7573
+
8273
=
1073
+
6773
+
8833
=
1973
+
5233
+
9473
=
2813
+
4193
+
9673
(see the number 185 527).
999 999 937
the largest nine digit prime number.
1 000 000 007
the smallest ten digit prime number.
1 053 422 339 (= 19 · 73 · 179 · 4243)
the 1 000 000
000th
composite number (see the number 133).
1 075 790 572
the smallest number n such that the Liouville function λ0 takes on successively,
starting with n, the values 1, −1, . . . , 1, −1
30 numbers in all
(see the number 6 185).
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