244 Jean-Marie De Koninck
164 499
the 100 000th square-free number (see the number 165).
165 701
the first member p of the second 7-tuple (p, p+2, p+6, p+8, p+12, p+18, p+20)
made up entirely of prime numbers: the smallest 7-tuple satisfying this property
is (11, 13, 17, 19, 23, 29, 31).
169 219
the smallest prime number p which is the first link of a
p2
+ 1 chain of order 5
(see the number 271).
171 893
the smallest number n such that τ (n) = τ (n + 1) = τ (n + 2) = τ (n + 3) =
τ (n + 4) = τ (n + 5) = τ (n + 6): here the common value is 8; the sequence
of numbers satisfying this property begins as follows: 171893, 180965, 647381,
1039493, 1071829, 1450261, 1563653, 1713413, . . . (see the number 33).
173 359
the smallest prime number p such that p + 70 is prime and such that each
number between p and p + 70 is composite (see the number 139).
174 592 (=
29
· 11 · 31)
the third solution of equation
σ(n)
n
=
9
4
(see the number 40).
175 197
the only number n such that π(n) = n/11 (see the number 330).
176 661 (= 3 · 258887)
the fourth 2-hyperperfect number (see the number 21).
177 833
the third number n 1 such that n2 + 3 is a powerful number: here 177 8332 +
3 =
22
·
72
·
133
·
2712
(see the number 37).
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