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).