206 Jean-Marie De Koninck
26 208 (= 25 · 32 · 7 · 13)
the third solution of
σ(n)
n
=
7
2
(see the number 4 320).
26 277 (= 3 · 19 · 461)
the number n which allows the sum
m≤n
ω(m)=3
1
m
to exceed 2 (see the number
1 953).
26 608 (=
24
· 1663)
the 10
000th
number having exactly two distinct prime factors (see the number
184).
26 861
the smallest number n for which π(n; 4, 1) π(n; 4, 3) (Leech, 1957).
26 951
the
19th
number n (and the largest one known) such that n! + 1 is prime (see
the number 116); note that the number 26 951! + 1 is a 107 707 digit number.
27 000
the fifth number n 2 such that
σ(n) + φ(n)
γ(n)2
is an integer (see the number
588).
27 625 (= 53 · 13 · 17)
the smallest number which can be written as the sum of two squares in seven
distinct ways (as well as in eight distinct ways), namely 27 625 =
202
+
1652
=
272 +1642 = 452 +1602 = 602 +1552 = 832 +1442 = 882 +1412 = 1012 +1322 =
1152 + 1202 (see the number 50).
27 720 (= 23 · 32 · 5 · 7 · 11)
the smallest number n such that σ(n) 4n: in this case,
σ(n)
n
4.05; the
sequence of numbers satisfying this property begins as follows: 27 720, 30 240,
32 760, 50 400, 55 440, 60 480, 65 520, 75 600, 83 160, . . . ; moreover, if n = nk
stands for the smallest number n such that σ(n) kn, then n2 = 6, n3 = 120,
n4 = 27 720, n5 = 122 522 400 and n6 = 130 429 015 516 800;
the 25th highly composite number (see the number 180).
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