Those Fascinating Numbers 339

1 303 324 906

• the smallest number n such that β(n) β(n + 1) . . . β(n + 11): here

1198 3190 5844 91691 753547 766221 4287274 118484094

217220824 260664988 325831231 434441642 (see the number 714).

1 375 298 099

• the smallest number which can be written as a sum of three distinct fifth powers

in two distinct ways: 1 375 298 099 =

245

+

285

+

675

=

35

+

545

+

625

(for the

sum of fourth powers, see the number 2 673; for the sum of distinct fourth

powers, see the number 5 978 883; see also the number 6 578).

1 379 454 720 (= 28 · 3 · 5 · 7 · 19 · 37 · 73)

• the seventh 4-perfect number (see the number 30 240): this number can be

obtained using the tri-perfect number 459 818 240 by observing that if n is

tri-perfect and (n, 3) = 1, then 3n is 4-perfect.

1 382 958 545

• the 15th Bell number (see the number 52).

1 419 138 368

• the second number which can be written as the sum of the fifth powers of three

numbers in two distinct ways:

1 419 138 368 =

135

+

515

+

645

=

185

+

445

+

665

(see the number 1 375 298 099).

1 433 272 320

• the fourth number which is equal to the product of the factorials of its digits in

base 7: 1 433 272 320= [5, 0, 3, 4, 2, 4, 2, 0, 3, 3, 4]7 = 5!·0!·3!·4!·2!·4!·2!·0!·3!·3!·4!

(see the number 248 832 000).

1 459 956 960 (=

25

·

34

· 5 ·

72

·

112

· 19)

• the second solution of

σ(n)

n

=

19

4

(see the number 746 444 160).

1 476 304 896 (=

213

· 3 · 11 · 43 · 127)

• the fifth tri-perfect number (see the number 120): Carmichael proved that it is

the only tri-perfect number with exactly five distinct prime factors.