Those Fascinating Numbers 345
3 569 485 920 (= 25 · 3 · 5 · 7 · 11 · 13 · 17 · 19 · 23)
the number n for which the expression
Ω(n)ω(n)
n
reaches its maximal value203,
namely 2.97088 (see the numbers 60 and 120 120).
3 663 002 302
the number of 11 digit prime numbers (see the number 21).
3 736 935 913
the smallest number n such that π(n)
6
j=1
(j 1)!n
logj
n
, this last expression
representing the first six terms of the asymptotic expansion of Li(n): here
π(3 736 935 913) = 178 046 624, while
∑6
j=1
(j−1)!n
logj
n
n=3 736 935 913
178 046 623.82 (see the number 73).
3 778 888 999
the smallest number of persistence 10 (see the number 679).
3 786 686 400
the
14th
number n such that φ(n) + σ(n) = 4n (see the number 23 760).
4 044 619 541
the smallest number n such that P (n) P (n + 1) . . . P (n + 12): here
4044619541 674103257 19168813 10317907 5737049 1447609
465809 451207 199429 162109 115399 82021 1913 (see the
number 1 851).
4 118 054 813
the number of prime numbers 1011.
203It
is easy to establish that this number n is of the form n =
2a−1p1p2
. . . pk for certain positive
integers a and k; one can then prove that the optimal choice is obtained by setting a = 5 and k = 9.
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