290 Jean-Marie De Koninck
5 096 876
the number of eight digit prime numbers (see the number 21).
5 099 011 (= 19 · 167 · 1607)
the number n which allows the sum
m≤n
ω(m)=3
1
m
to exceed 4 (see the number
1 953).
5 134 240
the largest number which is not the sum of distinct fourth powers (see Journal
of Recreational Mathematics 20 (1988), p. 316).
5 153 633
the smallest number which can be written as the sum of two fifth powers and
as the sum of five fifth powers: 5 153 633 =
15
+
225
=
45
+
55
+
75
+
165
+
215.
5 195 977
the smallest prime number q which allows the sum
p≤q
1
p
to exceed 3 (see the
number 277).
5 296 623 (= 3 · 1765541)
the number n which allows the sum
m≤n
Ω(m)=2
1
m
to exceed 4 (see the number 871).
5 315 625 (= 35 · 55 · 7)
the smallest number n having at least two distinct prime factors and such that
β(n)3 = B1(n): here (3 + 5 + 7)3 = 35 + 55 + 7 = 3375 (see also the number
5 120).
5 617 820
the smallest number n such that ω(n)+ω(n+1)+ω(n+2) = 16: here 5 617 820 =
22
·5·13·17·31·41, 5 617 821 = 3·11·37·43·107 and 5 617 822 = 2·7·29·101·137
(see the number 2 210).
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