Those Fascinating Numbers 325
197 064 960 (= 28 · 3 · 5 · 19 · 37 · 73)
the fifth solution of
σ(n)
n
=
7
2
(see the number 4 320).
199 360 981
the
14th
Euler number (see the number 272).
202 536 181
the smallest number n such that Ω(n) = Ω(n + 1) = . . . = Ω(n + 10): here the
common value is 4 (see the number 602).
205 962 976
the largest number n whose sum of digits is equal to
5

n (see the number
17 210 368).
208 565 280 (= 25 · 34 · 5 · 72 · 112 · 19)
the smallest solution of
σ(n)
n
=
14
3
; the second one is 240 589 440.
221 167 422
the smallest number n such that n, n+1, n+2, n+3, n+4, n+5, n+6, n+7, n+
8, n + 9, n + 10 are each divisible by a square 1: here 221 167 422 = 2 ·
35
·
7 · 65011, 221 167 423 =
312
· 230143, 221 167 424 =
26
· 3455741, 221 167 425 =
3 ·
52
· 23 · 128213, 221 167 426 = 2 ·
372
· 80777, 221 167 427 =
132
· 29 · 45127,
221 167 428 =
22
· 3 · 18430619, 221 167 429 =
73
· 19 · 33937, 221 167 430 = 2 · 5 ·
112
·47·3889, 221 167 431 =
32
·109·131·1721 and 221 167 432 =
23
·2099·13171
(see the number 242).
223 092 870 (= 2 · 3 · 5 · 7 · 11 · 13 · 17 · 19 · 23)
the number n which allows the quantity
ω(n)
log n/ log log n
to reach its maximal
value, namely 1.38402 . . . (see J.L. Nicolas [151]);
the only number n which does not satisfy inequality
n
φ(n)


log log n +
5
2 log log n
;
for this inequality to hold for n = 223 092 870, one must replace the fraction
5
2
by 2.50637 (see J.B. Rosser & L. Schoenfeld [178]).
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