Those Fascinating Numbers 111
882
the
15th
number n such that n ·
2n
1 is prime (see the number 115).
887
the prime number which appears the most often as the
11th
prime factor of an
integer (see the number 199);
the smallest prime number p such that p + 20 is prime and such that each
number between p and p + 20 is composite (see the number 139);
the smallest prime factor of the Mersenne number 2443 1, whose complete
factorization is given by
2443
1 = 887 · 207818990653657 · P117;
the second number which does not produce a palindrome by the 196-algorithm
(see the number 196).
891
the second odd number n 1 such that γ(n)|σ(n) (see the number 135).
906
the smallest number n such that inequality log g(m)

m log m holds for
all m n: here g(m) = max
σ∈Sm
(order of σ), where Sm stands for the group of
permutations of m (J.P. Massias [131]).
907
the smallest prime number which is preceded by 19 consecutive composite num-
bers; indeed, there is no prime number between 887 and 907.
911
the first component of the fifth pair of prime numbers {p, q} such that
pq−1
1 (mod
q2)
and
qp−1
1 (mod
p2);
here {p, q} = {911, 318917} (see the number 2 903).
915
the smallest odd number which can be written as the sum of some
powers117
of its prime factors: here 915 = 3 · 5 · 61 =
36
+
53
+
611.
117In
2005, J.M. De Koninck & F. Luca [54] studied the size of the set {n x : ω(n) 2 and n =
p|n
pαp }, where each exponent αp can vary with the prime divisor p.
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