Those Fascinating Numbers 263

523 776 (= 29 · 3 · 11 · 31)

• the third tri-perfect number (see the number 120).

524 160 (= 27 · 32 · 5 · 7 · 13)

• the smallest solution of

σ(n)

n

=

17

4

.

524 287 (= 219 − 1)

• the seventh Mersenne prime.

529 620

• the seventh number n such that φ(n)σ(n) is a fourth power: here

φ(529620)σ(529620) =

6724

(see the number 170).

531 434

• the second solution of σ(n + 7) = σ(n) + 7 (see the number 74).

540 857

• the fifth composite number n such that 2n−2 ≡ 1 (mod n); see the number

20 737.

542 603

• the smallest prime number p such that p + 80 is prime and such that each

number between p and p + 80 is composite (see the number 139).

545 835

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

548 834

• the only number 1 which can be written as the sum of the sixth powers of

its digits: 548 834 =

56

+

46

+

86

+

86

+

36

+

46.

548 856

• the eighth number n such that σ(φ(n)) = n (see the number 744).