230 Jean-Marie De Koninck
86 243
the exponent of the
28th
Mersenne prime
286 243
1 (Slowinski, 1982).
86 453
the seventh number k such that 11 . . . 1
k
is prime (Baxter, 2000); see the num-
ber 19.
87 360
one of the five known unitary perfect numbers (see the number 6).
87 750
the second number n such that (σI (n) + γ(n))/n is an integer (see the number
270).
87 890
the sixth number n such that each of the numbers n + i, i = 0, 1, 2, . . . , 16, has
a factor in common with the product of the other 16 (see the number 2 184).
88 799
the smallest prime factor of s13 = 11 +22 +33 + . . . +1313; in fact, s13 = 88799 ·
3514531963 (see the number 3 413 for the list of known numbers sn which are
prime); below is a table of the factorizations of the numbers 11 +22 +33 +. . .+nn
for 2 n 60:
n
11
+
22
+
33
+ . . . +
nn
2 5
3
25
4
25
·
32
5 3413
6 50069
7
22
·
33
· 8089
8
22
· 13 · 17 · 41 · 487
9 7 · 19 · 1451 · 2099
10 10405071317
11
23
· 29 · 1274641129
12
23
· 7 · 164496735539
13 88799 · 3514531963
14 32 · 432 · 53 · 829 · 15624709
15 22 · 32 · 7 · 5501 · 13649 · 23747111
16 22 · 11 · 17 · 3907 · 625111 · 10343539
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