160 Jean-Marie De Koninck
4 151
one of the seven numbers which can be written as the sum of the fifth powers
of its digits: 4 151 =
45
+
15
+
55
+
15
(see the number 4 150).
4 177
the tenth prime number p such that (3p 1)/2 is itself a prime number (see
the number 1 091).
4 179
the smallest number n such that ω(n)+ω(n+1)+ω(n+2)+ω(n+3) = 13: here
4 179 = 3 · 7 · 199, 4 180 = 22 · 5 · 11 · 19, 4 181 = 37 · 113 and 4 182 = 2 · 3 · 17 · 41
(see the number 987).
4 181
the smallest composite Fibonacci number whose rank is prime: F19 = 4 181 =
37 · 113.
4 253
the exponent of the
19th
Mersenne prime
24 253
1 (Hurwitz, 1961).
4 273
the smallest number n requiring ten iterations of the σI (n) function in order
to reach 1 (see the number 193).
4 297
the prime number which appears the most often as the
14th
prime factor of an
integer (see the number 199);
the smallest prime number p such that p + 30 is prime and such that each
number between p and p + 30 is composite (see the number 139);
the 14th prime number pk such that p1p2 . . . pk 1 is prime (see the number
317).
4 316
the second solution of σ2(n) = σ2(n + 8) (see the number 860).
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