Those Fascinating Numbers 241
141 121
the number of integer zeros of the function M(x) :=
n≤x
µ(n) located in the
interval [1,
109]
(see the number 92).
142 560
the ninth number n 1 such that φ(σ(n)) = n (see the number 128).
142 857
the smallest number which quintuples when its last digit is moved in first po-
sition173;
the first six decimals (and the period) of 1/7; indeed,
1
7
= 0.142857 142857 . . .
143 018
the
25th
number n such that n ·
2n
1 is prime (see the number 115).
145 823
the 20th prime number pk such that p1p2 . . . pk + 1 is prime (see the number
379).
147 492
the sixth number n such that φ(n) + σ(n) = 3n (see the number 312).
148 219 (= 19 · 29 · 269)
the smallest square-free composite number n such that p|n =⇒ p + 6|n + 6 (see
the number 399).
148 349
the only known number n which is equal to the sum of the sub-factorials of its
digits: 148 349 =!1+!4+!8+!3+!4+!9; the sub-factorial function !n is defined by
!n = n! 1
1
1!
+
1
2!

1
3!
+ . . . +
(−1)n
1
n!
.
173One
can prove that there exist infinitely many numbers satisfying this property by simply
considering the sequence of numbers 142 857, 142 857 142 857, 142 857 142 857 142 857, and so on.
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