Those Fascinating Numbers 275

1 042 404

• the smallest number n such that ω(n)+ω(n+1)+ω(n+2) = 15: here 1 042 404 =

22

· 3 · 11 · 53 · 149, 1 042 405 = 5 · 7 · 13 · 29 · 79 and 1 042 406 = 2 · 17 · 23 · 31 · 43

(see the number 2 210).

1 046 528

• the seventh number n divisible by a square 1 and such that γ(n+1)−γ(n) = 1

(see the number 48).

1 051 783

• the largest number which is equal to the sum of the squares of the factorials

of its digits in base 7: here 1 051 783 = [1, 1, 6, 4, 0, 2, 6, 5]7 =

1!2

+

1!2

+

6!2

+

4!2 + 0!2 + 2!2 + 6!2 + 5!2 (see the number 73).

1 063 300 (=

22

·

52

·

73

· 31)

• the smallest number n 1 which is not a perfect number and not a multiple

of 3, but which satisfies the condition γ(σ(n)) = γ(n).

1 068 701

• the first component p of the third 7-tuple (p, p+2, p+6, p+8, p+12, p+18, p+20)

made up entirely of prime numbers: the smallest 7-tuple satisfying this property

is (11, 13, 17, 19, 23, 29, 31), while the second is the one whose first component

is 165 701.

1 084 605 (= 3 · 5 · 72307)

• the 1 000

000th

composite number (see the number 133).

1 092 747

• the smallest number n such that n, n + 1, n + 2, n + 3, n + 4, n + 5, n + 6 and

n+7 are all divisible by a square 1: here 1 092 747 =

3·192

·1009, 1 092 748 =

22·273187,

1 092 749 =

72·29·769,

1 092 750 =

2·3·53·31·47,

1 092 751 =

113·821,

1 092 752 =

24

· 163 · 419, 1 092 753 =

32

· 23 · 5279 and 1 092 754 = 2 ·

132

· 53 · 61

(see the number 242).

1 099 989

• the seventh number which is not a palindrome, but which divides the number

obtained by reversing its digits (see the number 1 089).