172 Jean-Marie De Koninck
6 397
the prime number which appears the most often as the
15th
prime factor of an
integer (see the number 199).
6 399
the second solution of τ (n + 1) τ (n) = 17 (see the number 1 295).
6 435
the 11th odd abundant number (see the number 945).
6 451
the third prime number p such that
31p−1
1 (mod
p2)
(see the number 79).
6 474
the third solution of σ2(n) = σ2(n + 12) (see the number 864).
6 489
the smallest number n which allows the sum
m≤n
1
φ(m)
to exceed 17 (see the
number 177).
6 552 (=
23
·
32
· 7 · 13)
the third solution of
σ(n)
n
=
10
3
(see the number 1 080).
6 569
the
16th
prime number pk such that p1p2 . . . pk 1 is prime (see the number
317).
6 578
the smallest number which can be written as the sum of three distinct fourth
powers in two distinct ways: 6 578 =
14
+
24
+
94
=
34
+
74
+
84
(Martin,
1876); for the case when the condition “distinct” is not required, see the num-
ber 2 673; if nk stands for the smallest number n which can be written as
the sum of three distinct fourth powers in k distinct ways, then n2 = 6 578,
n3 = 811 538, n4 = 5 978 883, n5 = n6 = 292 965 218, n7 = 779 888 018 and
n8 = 5 745 705 602; for the analogue question with the fifth powers, see the
number 1 375 298 099; for the sixth powers, see the number 160 426 514;
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