Those Fascinating Numbers 279

1 456 728

• the smallest 6-composite number n such that n + 2 is also 6-composite: here

1 456 728 = 23 · 3 · 7 · 13 · 23 · 29 and 1 456 730 = 2 · 5 · 11 · 17 · 19 · 41 (see the

number 1 428).

1 570 153 (= 13 · 269 · 449)

• the smallest hyperperfect number having exactly three distinct prime factors

(it is the third 12-hyperperfect number).

1 571 328 (= 29 · 32 · 11 · 31)

• the third solution of

σ(n)

n

=

13

4

(see the number 360);

• the eighth Erd˝ os-Nicolas number (see the number 2 016).

1 590 816

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

1 630 622

• the eighth composite number n such that σ(n + 6) = σ(n) + 6 (see the number

104).

1 644 919

• the 1 000

000th

square-free number (see the number 165).

1 671 800

• the smallest multiple of 100 which is followed by at least 100 composite numbers

(see the number 370 261).

1 679 616

(=364)

• the largest number n whose sum of digits is equal to

4

√

n (see the number 2 401).

1 741 725

• the smallest number n 1 which can be written as the sum of the seventh

powers of its digits: the others are 4 210 818, 9 800 817, 9 926 315 and 14 459 929.