Those Fascinating Numbers 141
2 007
the sixth number n such that
2n
+
n2
is a prime number: the only numbers
n 30 000 satisfying this
property138
are 3, 9, 15, 21, 33, 2 007, 2 127, 3 759
and 29 355.
2 015
the third Lucas-Carmichael number (see the number 399).
2 016 (=
25
·
32
· 7)
the second Erd˝ os-Nicolas number, that is a number n which is not perfect, but
for which there exists a number m such that

d|n, d≤m
d = n; the sequence
of numbers satisfying this property begins as follows: 24, 2 016, 8 190, 42 336,
45 864, 392 448, 714 240, 1 571 328 . . . (with no others 2 · 107); see P. Erd˝ os &
J.L. Nicolas [78];
the second solution of
σ(n)
n
=
13
4
(see the number 360).
2 041 (= 13 · 157)
the second 12-hyperperfect number (see the number 697).
2 047
the smallest composite Mersenne number: 2 047 =
211
1 = 23 · 89;
the smallest strong pseudoprime in base 2: an odd composite number n, with
(a, n) = 1 and n 1 =
2s
· d, d odd, is said to be a strong pseudoprime in base a
if
ad
1 (mod n) or if
a2r
d
−1 (mod n) for a certain integer r [0, s −1].
2 053
the
11th
known prime number pk such that p1p2 . . . pk 1 is prime (see the
number 317).
2 056
the value of the sum of the elements of a diagonal, of a line or of a column in
a 16 × 16 magic square (see the number 15).
138It is easy to check that such a number n is necessarily of the form 6k + 3.
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