Those Fascinating Numbers 271
823 544 (= 23 · 113 · 911)
the seventh number of the form
nn
+ 1 (see the number 3 126).
825 265 (= 5 · 7 · 17 · 19 · 73)
the smallest Carmichael number which is the product of five prime numbers:
it is the
40th
Carmichael number (see the number 41 041).
838 561
the smallest prime number p such that Ω(p+1) = 2, Ω(p+2) = 3, Ω(p+3) = 4,
Ω(p + 4) = 5 and Ω(p + 5) = 6 (see the number 61).
846 137
the smallest prime number amongst those which appear more often as the fourth
prime factor of an integer than as the third prime factor; more precisely, when
846 137 appears in the prime factorization of a number, then in 24.547684% of
the cases, it is as the fourth prime factor of that number, while it is as the third
one in 24.547676% of the cases, the fifth in 17.16% of the cases and the sixth
in only 9% of the
cases186.
859 433
the exponent of the
33rd
Mersenne prime
2859 433
1 (Slowinski, 1993).
873 612
the value of
11
+
22
+ . . . +
77
(see the number 3 413).
874 660 (=
22
· 5 · 101 · 433)
the smallest number n which allows the sum
m≤n
Ω(m)=5
1
m
to exceed 1; if nk stands
for the smallest number n = nk which allows the sum
m≤n
Ω(m)=k
1
m
to exceed
1, then n1 = 5, n2 = 35, n3 = 402, n4 = 10 305, n5 = 874 660 and n6 =
395 096 427.
186This
characterization of 846 137 can be obtained from the results found in J.M. De Koninck &
G. Tenenbaum [63].
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