114 Jean-Marie De Koninck
954
the only three digit self replicating number: a number n all of whose digits are
distinct and decreasing is said to be self replicating if the process of reversing
its digits and subtracting this new number from the number n yields a number
whose digits are the same as that of n: no numbers with 1, 2, 5, 6 or 7 digits
satisfy this property; see M. Gardner [87]; the numbers 954, 7 641, 98 754 210,
987 654 321 and 9 876 543 210 are the only ones satisfying this property.
957
the third solution of σ(n) = σ(n + 1) (see the number 14).
959
the
13th
number k such that
k|(10k+1
1) (see the number 303).
960
the fourth number n divisible by a square 1 and such that γ(n+1)−γ(n) = 1
(see the number 48);
the fifth number which is equal to the sum of its digits added to the sum of the
cubes of its digits: the only numbers satisfying this property are 12, 30, 666,
870, 960 and 1 998.
968
the only solution n
1012
of σ(n) = 2n + 59 (see the number 196);
the second powerful number which can be written as the sum of two co-prime
3-powerful numbers = 1: 968 = 343 + 625, that is
23
·
112
=
73
+
54
(see the
number 841).
971
the largest irregular prime smaller than 1000 (see the number 59).
974
the
17th
number n such that n! 1 is prime (see the number 166).
975
the tenth solution of φ(n) = φ(n + 1) (see the number 15).
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