Those Fascinating Numbers 245
178 101
the smallest number which is not a fifth power, but which can be written as the
sum of the fifth powers of some of its prime factors: here 178 101 =
32
· 7 · 11 ·
257 =
35
+
75
+
115
(see the number 870); at least five other numbers satisfy
this property, namely 3 077 237 625, 114 190 363 548 900, 1 067 104 211 610 690,
2 974 846 981 587 921 076 and 292 100 153 292 936 484 034.
179 487
the fourth number which quadruples when its last digit is moved in first position
(see the number 102 564).
179 951
the smallest prime factor of the Mersenne number
259
1, whose complete
factorization is given by
259
1 = 179951 · 3203431780337.
180 246
the sixth number n such that 2n −2 (mod n) (see the number 946).
182 182
the seventh number n divisible by a square 1 and such that δ(n+1)−δ(n) = 1
(see the number 49).
183 091
the first term of the smallest sequence of ten consecutive prime numbers all of
the form 4n + 3 (see the number 463).
185 527
the smallest number which can be written as the sum of the cubes of three
distinct prime numbers in two distinct ways: here
185 527 =
193
+
313
+
533
=
133
+
433
+
473;
if nk stands for the smallest number which can be written as the sum of the
cubes of three distinct prime numbers in k distinct ways, then n2 = 185 527,
n3 = 8 627 527 and n4 = 999 979 163.
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