192 Jean-Marie De Koninck
14 722
the smallest number which can be written as the sum of two distinct fourth
powers and as the sum of four distinct fourth powers: 14 722 =
34
+
114
=
14 + 54 + 84 + 104; the sequence of numbers satisfying this property begins as
follows: 14722, 32657, 49297, 132722, 198577, 235552, 300577, 393026, . . .
14 833
the number of possible arrangements of the integers 1,2,. . . ,8 with the restric-
tion that the integer j must not be in the
jth
position for each j, 1 j 8
(see the number 265).
14 841
the tenth solution of σ(n) = σ(n + 1) (see the number 206).
14 884
the second powerful number which can be written as the sum of two co-prime
4-powerful numbers: 14 884 = 243 + 14 641, that is
22
·
612
=
35
+
114
(see the
number 12 769);
the eighth powerful number which can be written as the sum of two co-prime
3-powerful numbers = 1: 14 884 = 243 + 14 641, that is
22
·
612
=
35
+
114
(see
the number 841).
15 015 (= 3 · 5 · 7 · 11 · 13)
the smallest odd square-free abundant number.
15 120
the 22nd highly composite number (see the number 180).
15 121
the smallest prime number p such that Ω(p +1) = 2, Ω(p +2) = 3, Ω(p +3) = 4
and Ω(p + 4) = 5 (see the number 61).
15 193
the smallest prime factor of the Mersenne number
2211
1, whose complete
factorization is given by
2211
1 = 15193 · 60272956433838849161
·3593875704495823757388199894268773153439.
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