Those Fascinating Numbers 179
8 638
(probably) the largest number which cannot be written as the sum of two co-
prime numbers whose index of composition is 1.7 (see the number 933).
8 646
the fifth number n such that 2n −2 (mod n) (see the number 946).
8 648
the eighth dihedral perfect number (see the number 130).
8 672
the smallest solution y of y2 =
(
x
0
)
+
(
x
1
)
+
(
x
2
)
+
(
x
3
)
, namely (x, y) = (767, 8672)
(see the number 767).
8 786
the smallest solution of σ(n) = σ(n + 69): it is mentioned in R.K. Guy [101],
B13, that Mientka and Vogt could only find two solutions of this equation,
namely 8 786 and 24 885: but there are 35 more
107;
the sequence of num-
bers satisfying this property begins as follows: 8786, 24885, 205206, 274505,
414645, 554826, 622686, 724746, . . .
8 825
the third composite number n (and the largest one known) such that σ(n +
2) σ(n) = 2 (see the number 434).
8 855
the eighth Lucas-Carmichael number (see the number 399).
8 911 (= 7 · 19 · 67)
the seventh Carmichael number (see the number 561).
8 922
the second solution of σ(n) = σ(n + 3) (see the number 382).
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