Those Fascinating Numbers 323

143 123 843

• the fifth number which can be written in two distinct ways as the sum of two

co-prime numbers with an index of composition ≥ 5: 143123843 =

212

·

55

+

33

·

136

=

235

+

22

·

37

·

56,

each of these last four numbers having as index

of composition 7.10721, 5.10037, 5 and 5.50783 respectively (see the number

371 549).

146 511 208

• the smallest number n 1 which is equal to the sum of the ninth powers of its

digits: the only other numbers n 1 satisfying this property are 472 335 975,

534 494 836 and 912 985 153.

150 441 856

• the 18th dihedral perfect number (see the number 130).

153 587 720

• the

21rst

number n such that φ(n) + σ(n) = 3n (see the number 312).

158 385 500

• the third number n such that P

(n)2|n,

P (n +

1)2|n

+ 1 and P (n +

2)2|n

+ 2:

here 158 385 500 =

22

·

53

· 7 · 13 ·

592,

158 385 501 =

32

·

192

· 29 ·

412

and

158 385 502 = 2 · 11 · 109 ·

2572

(see the number 1 294 298).

160 426 514

• the smallest number which can be written as the sum of three distinct sixth

powers in two distinct ways: 160 426 514 = 36 + 196 + 226 = 106 + 156 + 236;

the sequence of numbers satisfying this property begins as follows: 160 426 514,

10 267 296 896, 95 200 890 914, 116 950 928 706, 176 277 173 474, 289 824 641 354,

300 620 262 890, 657 107 001 344, . . . (see the number 6 578).

167 772 161

• the smallest prime factor of F23 =

2223

+ 1 (see the number 70 525 124 609).

169 674 751

• the smallest prime number p such that Ω(p − 1) = Ω(p + 1) = 13: here

169 674 750 = 2 ·

36

·

53

·

72

· 19 and 169 674 752 =

211

· 13 · 6373 (see the

number 271).