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).
Previous Page Next Page