324 Jean-Marie De Koninck

171 078 830 (= 2 · 5 · 13 · 23 · 29 · 1973)

• the smallest abundant number n such that n + 1 and n + 2 are also abundant;

the sequence of numbers satisfying this property begins as follows: 171 078 830,

268 005 374, 321 893 648, 336 038 624, 487 389 824, . . .

173 706 136

• the

19th

dihedral perfect number (see the number 130).

179 376 463

• the smallest number n such that the Liouville function λ0 takes successively,

starting with n, 30 times in a row, the value −1 (see the number 5 879).

179 390 821

• the 10 000

000th

prime power, in fact here a prime number (see the number

419).

179 424 673

• the 10 000 000th prime number (see the number 541).

182 403 491

• the first member p of the second 9-tuple (p, p + 2, p + 6, p + 8, p + 12, p + 18, p +

20, p+26, p+30) made up entirely of prime numbers: the first 9-tuple satisfying

this property is (11,13,17,19,23,29,31,37,41).

184 055 430

• the smallest number n such that ω(n) + ω(n + 1) + ω(n + 2) = 18: here

184 055 430 = 2 · 3 · 5 · 13 · 172 · 23 · 71, 184 055 431 = 7 · 29 · 47 · 101 · 191 and

184 055 432 = 23 · 11 · 19 · 31 · 53 · 67 (see the number 2 210).

184 773 312

• the fourth number n (and the largest one known) such that σ(n) = 3n + 12;

the three smallest are 780, 2 352 and 430 272.

190 899 322

• the

14th

Bell number (see the number 52).