260 Jean-Marie De Koninck
432 000
the tenth number n 2 such that
σ(n) + φ(n)
γ(n)2
is an integer (see the number
588).
435 708 (=
22
·
32
·
72
· 13 · 19)
the fourth solution of
σ(n)
n
=
10
3
(see the number 1 080).
440 312
the number of twin prime pairs
108
(see the number 1 224).
441 461
the
13th
and largest prime number q for which the value of the corresponding
sum

p≤q
p uses each of the digits 0,1,2,. . . ,9 once and only once: in this case,

p≤441461
p = 7 803 615 924 (see the number 155 863).
453 962
the eighth number n divisible by a square 1 and such that δ(n +1)−δ(n) = 1
(see the number 49).
455 226
the smallest number which is equal to the sum of the seventh powers of its digits
added to the product of its digits: the only numbers satisfying this property
are 455 226, 3 653 786, 4 210 818, 7 774 369 and 9 800 817.
461 890
the smallest integer n such that ω(n), ω(n + 1), . . . , ω(n + 5) are all distinct,
namely in this case with the values 6, 1, 4, 2, 3 and 5 (see the number 417).
465 124
the eighth powerful number n such that n + 1 is also powerful: here 465 124 =
22 · 112 · 312 and 465 125 = 53 · 612 (see the number 288).
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