252 Jean-Marie De Koninck
265 826
the eighth number n such that
2n
−2 (mod n) (see the number 946).
266 401
the second number n such that φ(n), φ(n + 1), φ(n + 2), φ(n + 3) and φ(n + 4)
have the same prime factors, namely here 2, 3, 5 and 37: the sequence of num-
bers satisfying this property begins as follows: 35, 266 401, 995 402, 1 299 600,
2 352 240, . . . ; if nk stands for the smallest number n such that φ(n), φ(n + 1),
. . . , φ(n + k) have the same prime factors, then n1 = 3, n2 = 3, n3 = n4 = 35
and n5 = 43 570 803 (see also the number 3 777).
270 343
the largest known number k such that 11 . . . 1
k
is prime (discovered by Voznyy
and Budnyy in 2007); see the number 19.
271 441
the smallest composite number n such that n|℘(n), where (℘(n))n≥0 stands for
the sequence of Perrin numbers defined by ℘(0) = 3, ℘(1) = 0, ℘(2) = 2 and
for each n 3 by ℘(n) = ℘(n 2) + ℘(n 3); Perrin observed in 1899 that if
n is prime, then n|℘(n) (see E. Weisstein [201], p. 1351).
273 524
the third number n such that Eφ(n) := φ(n + 1) φ(n) satisfies Eφ(n + 1) =
Eφ(n): here the common value of is −480, since φ(273 524) = 125 280,
φ(273 525) = 124 800 and φ(273 526) = 124 320 (see the number 5 312).
274 177
the smallest prime factor of the Fermat number F6 =
226
+ 1 (see the number
70 525 124 609).
274 505
the fourth solution of equation σ(n) = σ(n + 69) (see the number 24 885).
282 489
the smallest number n such that ω(n) + ω(n + 1) + ω(n + 2) + ω(n + 3) = 17:
here 282 489 = 3 · 17 · 29 · 191, 282 490 = 2 · 5 · 13 · 41 · 53, 282 491 = 11 · 61 · 421
and 282 492 = 22 · 32 · 7 · 19 · 59 (see the number 987).
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