320 Jean-Marie De Koninck

100 210 581

• the smallest number n which allows the sum

i≤n

1

i

to exceed 19 (see the number

83).

100 651 008 (= 212 · 3 · 8191)

• the sixth solution of

σ(n)

n

=

8

3

(see the number 1 488).

102 247 563

• the tenth horse number (see the number 13).

102 345 689

• the smallest prime number made up of nine distinct digits (see the number

1 039).

102 435 795

• the sixth solution of σ(n) = σ(n + 15) (see the number 26).

104 986 323

• the smallest number which can be written as the sum of three fourth powers of

prime numbers in two distinct ways: here

104 986 323 =

74

+

314

+

1014

=

614

+

734

+

894;

the sequence of numbers satisfying this property begins as follows: 104 986 323,

127 104 003, 127 494 003, 294 141 603, 401 979 123, 1 228 623 123, 2 046 481 203,. . .

(see also the number 185 527 for the analogue question with cubes).

105 639 091

• the first term of the smallest sequence of 17 consecutive prime numbers all of

the form 4n + 3 (see the number 463).

106 091 745 (= 3 · 5 · 113 · 62591)

• the 100 000 000th composite number (see the number 133).