110 Jean-Marie De Koninck
n6 = 594 839 010 = 2 · 3 · 5 · 17 · 29 · 37 · 1087 =
26
+
56
+
296,
n7 = 275 223 438 741 = 3 · 23 · 43 · 92761523 =
37
+
237
+
437,
n8 = 26 584 448 904 822 018 = 2 · 3 · 7 · 17 · 19 · 113 · 912733109
=
28
+
178
+
1138,
n9 = 40 373 802 = 2 ·
34
· 7 · 35603 =
29
+
39
+
79,
n10 = 420 707 243 066 850 = 2 ·
32
·
52
· 29 · 32238102917
=
210
+
510
+
2910;
the fourth number which is equal to the sum of its digits added to the sum of
the cubes of its digits: one can easily prove that the only numbers satisfying
this property are 12, 30, 666, 870, 960 and 1 998.
871
the smallest number n which allows the sum
m≤n
Ω(m)=2
1
m
to exceed 2; if, given
k 1, nk stands for the smallest number n which allows this sum to exceed k,
then the sequence (nk)k≥1 begins as follows: 35, 871, 43 217, 5 296 623, . . .
872
the
16th
number n such that n! + 1 is prime (see the number 116).
873
the value of 1! + 2! + 3! + 4! + 5! + 6!.
877
the seventh Bell number (see the number 52).
880
the number of 4 × 4 magic squares (excluding rotations and reflections); if nk
stands for the number of k × k magic squares, then n1 = 1, n2 = 0, n3 = 1,
n4 = 880 and n5 = 275 305 224: this last value was obtained by R. Schroeppel
in 1973.
881
the largest known prime number p such that P
(p2
−1) = 11, where P (n) stands
for the largest prime factor of n (see the number 4 801).
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