Those Fascinating Numbers 277

1 221 858

• the smallest number having more than three distinct prime factors and which

is divisible by the cube of the sum of its prime factors: the sequence of num-

bers satisfying this property begins as follows: 1 221 858, 2 406 250, 2 443 716,

2 457 000, 3 346 110, 3 622 080, 3 665 574, . . . (see the number 37 026).

1 257 787

• the exponent of the

34th

Mersenne prime

21 257 787

− 1 (Slowinski, 1996).

1 258 500

• the smallest number n such that P (n + i) ≤

√

n + i for i = 0, 1, 2, 3, 4, 5, 6, 7,

8; the largest prime factors of these nine numbers are respectively 31, 23, 251,

971, 599, 857, 179, 367 and 1117, all smaller than

√

1258500 ≈ 1121 (see the

number 1 518).

1 294 298

• the smallest number n such that P

(n)2|n,

P (n +

1)2|n

+ 1 and P (n +

2)2|n

+ 2:

here we have 1 292 298 = 2 · 61 · 1032, 1 292 299 = 34 · 19 · 292 and 1 292 300 =

22 ·52 ·7·432; the sequence of numbers satisfying this property begins as follows:

1 294 298, 9 841 094, 158 385 500, 1 947 793 550, . . .

1 295 953

• the 100

000th

prime power, in fact here a prime number (see the number 419).

1 296 378

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

in six distinct ways:

1 296 378 =

33

+

763

+

953

=

93

+

333

+

1083

=

213

+

773

+

943

=

313

+

593

+

1023

=

333

+

813

+

903

=

603

+

753

+

873

(see the number 1 009).

1 299 709

• the 100 000th prime number (see the number 541).

1 304 498

• the smallest number n such that π(n) = n/13 (see the number 330).