326 Jean-Marie De Koninck
224 376 048
the number of twin prime pairs 1011 (see the number 1 224).
240 589 440 (=
27
·
35
· 5 · 7 · 13 · 17)
the second solution of
σ(n)
n
=
14
3
(see the number 208 565 280).
248 832 000
the smallest number 2 which is equal to the product of the factorials of its
digits in base 7: 248 832 000= [6, 1, 1, 1, 0, 1, 5, 5, 0, 4]7 = 6! · 1! · 1! · 1! · 0! · 1! · 5! ·
5! · 0! · 4!; the only known numbers satisfying this property are 1, 2, 248 832 000,
1 433 272 329, 15 407 021 574 586 368 000,
1 831 607 359 566 125 048 834 492 989 440 000 000 000 and
273 457 513 497 334 816 890 950 735 729 000 448 000 000 000 000 (see the number
17 280 for the list of the smallest numbers with this property in different bases).
257 400 763
the sixth number which can be written in two distinct ways as the sum of
two co-prime numbers each with an index of composition 5: 257 400 763 =
53 · 77 + 25 · 136 = 212 · 52 + 37 · 76, each of these last four numbers having as
index of composition 5.18928, 5.78725, 5.0103 and 6.36085 respectively (see the
number 371 549).
258 474 216
the largest triangular number which is the product (Anglin [6], p. 21) of three
consecutive numbers:
258 474 216 = 636 · 637 · 638 =
22 736 · 22 737
2
.
263 215 633
the number n which allows the sum
m≤n
ω(m)=1
1
m
to exceed 4 (see the number
1 307).
272 400 600
the smallest number n which allows the sum
i≤n
1
i
to exceed 20 (see the number
83).
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