Those Fascinating Numbers 159
3 913
the second square-free composite number n such that p|n =⇒ p + 2|n + 2 (see
the numbers 598 and 399).
3 994
the rank of the prime number which appears the most often as the
19th
prime
factor of an integer : p3994 = 37 717 (see the number 199).
4 030
the third bizarre number (see the number 70).
4 093
the
13th
prime number pk such that p1p2 . . . pk 1 is prime (see the number
317).
4 095
the largest triangular number of the form 2r 1: here 4 095 = 212 1 =
90·91
2
;
there exist only four numbers satisfying this property, the other three being
21 1, 22 1 =
2·3
2
and 24 1 =
5·6
2
;
the smallest number n such that 8! divides 1+2+ . . . + n (see the number 224);
the sixth odd abundant number (see the number 945).
4 104
the second number which can be written as the sum of two cubes in two distinct
ways: 4 104 =
23
+
163
=
93
+
153
(see the number 1 729).
4 140
the eighth Bell number (see the number 52).
4 150
the smallest number n 1 which can be written as the sum of the fifth powers of
its digits: 4 150 = 45 + 15 + 55 + 05; the only numbers satisfying this property
are 1, 4 150, 4 151, 54 748, 92 727, 93 084 and 194 979; if nk stands for the
smallest number n 1 which can be written as the sum of the k-th power of
its digits, then n3 = 153, n4 = 1 634, n5 = 4 150, n6 = 548 834, n7 = 1 741 725,
n8 = 24 678 050, n9 = 146 511 208 and n10 = 4 679 307 774.
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