Those Fascinating Numbers 291
5 761 455
the number of prime numbers
108.
5 761 978
the fifth even number n such that σI (n) = σI (n + 2) (see the number 54 178).
5 909 560
the smallest number n such that P (n)
5

n and P (n + 1)
5

n + 1: here
P (5909560) = P
(28
·
35
· 5 · 19) = 19 22.61 5

5909560 and P (5909561) =
P
(112
·
132
·
172)
= 17 22.61 5

5909561; the sequence of numbers satis-
fying this property begins as follows: 5909560, 11859210, 71843750, 76271624,
80061344, 96059600, 119094299, 132663167, 133919999, 177182720,
181037024,. . . (see the number 2
400)189.
5 978 882
the smallest number which can be written as the sum of three distinct fourth
powers in four distinct ways:
5 978 882 =
34
+
404
+
434
=
84
+
374
+
454
=
154
+
324
+
474
=
234
+
254
+
484
(see the number 6 578).
6 082 047
the smallest number n such that n and n+1 each have 11 prime factors counting
their multiplicity: 6 082 047 =
310
· 103 and 6 082 048 =
29
· 7 · 1697 (see the
number 135).
6 197 024
the smallest number n such that φ(6n+1) φ(6n+2) (see D.J. Newman [149]).
6 303 734
the fourth number n such that Eσ(n) := σ(n + 1) σ(n) satisfies Eσ(n + 1) =
Eσ(n): here the common value of is 1 429 056, since σ(6303734) = 9656928,
σ(6303735) = 11085984 and σ(6303736) = 12515040 (see the number 693).
6 436 343
the smallest fifth power which can be written as the sum of seven fifth powers:
6 436 343 =
235
=
15
+
75
+
85
+
145
+
155
+
185
+
205.
189This sequence is infinite: see the footnote tied to the number 2 400.
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