276 Jean-Marie De Koninck
1 109 549
(probably) the largest number which cannot be written as the sum of two co-
prime numbers whose index of composition is 1.9 (see the number 933).
1 122 112
the third insolite number (see the number 111).
1 122 659
the smallest prime number q1 such that each number qi = 2qi−1 + 1 is prime
for i = 2, 3, . . . , 7: such a sequence of prime numbers is called a Cunningham
chain (R.K. Guy [101], A7).
1 133 759
the smallest number n for which the µ function takes successively, starting with
n, the values 1,0,1,0,1,0,1,0,1,0,1,0,1; it is also the smallest number n for which
the µ function takes successively the values 1,0,1,0,1,0,1,0,1,0,1,0,1,0 (as well
as 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1); see the number 3 647.
1 140 480
the
11th
number n 1 such that φ(σ(n)) = n (see the number 128).
1 156 000 (= 25 · 53 · 172)
the number, amongst those 108, whose index of composition is the nearest to
the Euler number e: λ(1156000) 2.71827 (see the number 93 112 129 088 for
an even better approximation, and see the number 81 675 000 for the analogue
question with the number π)187.
1 164 241
the third star number n 1 which is also a perfect square (see the number
121).
1 190 400
the
12th
number n 1 such that φ(σ(n)) = n (see the number 128).
187In 2001, P. Ribenboim [170] proved that the set {λ(n) : n 1} is dense in the set of real numbers
r 1. It follows that for each real number r 1, there exists a sequence of positive integers nk
such that limk→∞ λ(nk) = r.
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