Those Fascinating Numbers 233

91 380

• the smallest number n which allows the sum

i≤n

1

i

to exceed 12.

92 274

• the seventh number n such that each of the numbers n + i, i = 0, 1, 2, . . . , 16,

has a factor in common with the product of the other 16 (see the number 2 184).

92 378

• the smallest number n such that ω(n) + ω(n + 1) + ω(n + 2) = 13: here

92 378 = 2 · 11 · 13 · 17 · 19, 92 379 = 3 · 7 · 53 · 83 and 92 380 =

22

· 5 · 31 · 149

(see the number 2 210).

92 727

• one of the seven numbers which can be written as the sum of the fifth powers

of its digits: 92 727 =

95

+

25

+

75

+

25

+

75

(see the number 4 150).

93 084

• one of the seven numbers which can be written as the sum of the fifth powers

of its digits: 93 084 =

95

+

35

+

05

+

85

+

45

(see the number 4 150).

93 527

• the second composite number n such that

2n−2

≡ 1 (mod n) (see the number

20 737).

95 220

• the tenth number n such that σ(n) and σ2(n) have the same prime factors,

namely the primes 2, 3, 7, 13 and 79 (see the number 180).

95 428

• the number of Niven numbers ≤ 106 (see the number 213).

95 800

• the first member of the first 4-tuple (x, y, z, t), such that x4 + y4 + z4 = t4: here

x = 95 800, y = 217 519, z = 414 560 and t = 422 481 (Elkies, 1988).