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 Eσ 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).