188 Jean-Marie De Koninck
12 168 (= 23 · 32 · 132)
the second powerful number n such that n 1 is a cube, namely
233;
the
smallest number n satisfying this property is 9, and there are no others
1015.
12 213
the largest known number n such that
2n
n is prime (see the number 261).
12 251
the
34th
Lucas prime number (see the number 613).
12 367
the smallest number n which allows the sum
i≤n
1
i
to exceed 10 (see the number
83).
12 379
the
19th
number n such that n ·
2n
1 is prime: in fact, it is the third prime
number n satisfying this property, the second being 751, and the first being 3
(see the number 115).
12 546
the number of integer zeros of the function M(x) :=
n≤x
µ(n) in the interval
[1,
107]
(see the number 92).
12 558 (= 2 · 3 · 7 · 13 · 23)
the eighth ideal number (see the number 390).
12 719
the ninth Lucas-Carmichael number (see the number 399).
12 721
the smallest number n such that P (n) P (n + 1) . . . P (n + 6): for
this number n, we also have P (n) P (n + 1) . . . P (n + 7), that is
12721 6361 4241 3181 509 101 89 43 (see the number 1 851).
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