336 Jean-Marie De Koninck
852 133 201
the smallest prime factor of the Mersenne number 2157 1, whose complete
factorization is given by
2157
1 = 852133201 · 60726444167 · 1654058017289 · 2134387368610417;
it is the smallest Mersenne number with four prime factors (see the number
223).
865 950 624
the tenth number n such that φ(n) + σ(n) = 4n (see the number 23 760).
880 346 227
the smallest number n such that λ0(n) = λ0(n + 1) = . . . = λ0(n + 28) = 1,
where λ0 stands for the Liouville function; moreover, for this n, we also have
λ0(n + 29) = λ0(n + 30) = 1 (see the number 1 934).
893 648 277 (=
193
· 130 303)
the fourth 18-hyperperfect number (see the number 1 333).
904 683 264
the
23rd
number n such that φ(n) + σ(n) = 3n (see the number 312).
906 150 256
the tenth number x such that

n≤x
λ0(n) = 0 (M. Tanaka [192]), where λ0
stands for the Liouville function.
906 150 257
the smallest number x 1 such that

n
λ0(n) 0, where λ0 stands for the
Liouville function (P´ olya believed that
∑≤x
n≤x
λ0(n) 0 for all numbers x 1):
here

n≤906150257
λ0(n) = 1 (see R.S. Lehman [123]).
912 985 153
the largest number equal to the sum of the ninth powers of its digits (see the
number 146 511 208).
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