Those Fascinating Numbers 301
15 913 724
the fifth number n such that Eσ(n) := σ(n + 1) σ(n) satisfies to Eσ(n +
1) = Eσ(n): here the common value of is −1 538 208, since σ(15913724) =
27849024, σ(15913725) = 26310816 and σ(15913726) = 24772608 (see the num-
ber 693).
16 449 370
the 10 000
000th
square-free number (see the number 165).
16 467 033
the smallest number n such that n, n+1 and n+2 are square-free and each have
five distinct prime factors: 16 467 033 = 3·11·17·149·197, 16 467 034 = 2·19·23·
83·227 and 16 467 035 = 5·13·37·41·167; the sequence of numbers satisfying this
property begins as follows: 16467033, 18185869, 21134553, 21374353, 21871365,
22247553, 22412533, 22721585, 24845313, 25118093, . . . (see the number 1 309).
16 777 217 (= 97 · 257 · 673)
the eighth number of the form
nn
+ 1 (see the number 3 126).
17 210 368 (=
285)
the smallest number n 1 whose sum of digits is equal to
5

n: the only
other numbers n 1 satisfying this property are 52 521 875, 60 466 176 and
205 962 976.
17 428 320
the second solution of
σ(n)
n
=
9
2
(see the number 8 910 720).
17 650 828
the value of 11 + 22 + . . . + 88 (see the number 3 413).
17 681 491
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 103).
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