266 Jean-Marie De Koninck
629 693
the smallest number n such that min(λ(n), λ(n + 1), λ(n + 2), λ(n + 3))
4
3
:
here
min(λ(n), λ(n + 1), λ(n + 2), λ(n + 3))
min(1.54162, 1.78225, 1.53833, 1.35053) = 1.35053;
the sequence of numbers satisfying this property begins as follows: 629 693,
11 121 381, 16 176 510, 20 188 925, 26 315 199, 82 564 351, 148 629 247, 185 966 873,
283 760 125, 1 791 156 975, 1 972 524 741, 3 047 548 776, . . . ; most likely there ex-
ist infinitely many numbers n satisfying this inequality (see for that matter the
number 14 018 750 and its footnote).
632 501
the smallest prime number q such that

p≤q
p is a multiple of 100 000: here

p≤632 501
p = 15 570 900 000 (see the number 35 677).
636 416
the smallest number n such that n and n + 1 are both divisible by an eighth
power: here 636 416 = 29 · 11 · 113 and 636 417 = 38 · 97 (see the number 1 215).
664 579
the number of prime numbers 10 000 000.
665 857
the 14th number n such that n2 1 is powerful: here
665
8572
1 =
29
·
32
·
172
·
5772
(see the number 485).
667 071
the
27th
and largest known number n such that n ·
2n
1 is prime (see the
number 115).
671 345
the smallest number n such that
f(n + 1) = f(n + 2) = f(n + 3) = f(n + 4) = f(n + 5) = f(n + 6),
where f(n) stands for the product of the exponents in the factorization of n
(see the number 843).
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