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.