248 Jean-Marie De Koninck
213 444 (= 3622)
the second perfect square whose last three digits are 444 (see the number 1 444).
214 195
the third number n such that σ(n), σ(n + 1), σ(n + 2), σ(n + 3) and σ(n + 4)
have the same prime factors, namely here 2, 3, 5, 7 and 17 (see the numbers
3 777 and 20 154).
214 273 (= 472 · 97)
the smallest 31-hyperperfect number (see the number 21).
214 369 (=
4632)
the smallest powerful number n such that n + 6 is also powerful: here n + 6 =
54 · 73; the sequence of numbers satisfying this property begins as follows:
214369, 744769, 715819215721, . . . 175 (see the number 463).
215 326
the second even number n such that
2n
2 (mod n) (see the number 161 038).
215 622
the ninth number n 2 such that
σ(n) + φ(n)
γ(n)2
is an integer (see the number
588).
216 091
the exponent of the
31rst
Mersenne prime
2216 091
1 (Slowinski, 1985).
217 070
the smallest number n such that n, n + 1, n + 2, n + 3, n + 4, n + 5 and n + 6 are
all divisible by a square 1: here 217 070 = 2 · 5 ·
72
· 443, 217 071 =
32
· 89 · 271,
217 072 =
24
· 13567, 217 073 = 17 ·
1132,
217 074 = 2 · 3 ·
112
· 13 · 23, 217 075 =
52
· 19 · 457 and 217 076 =
22
· 54269 (see the number 242).
175This sequence is infinite, since in 1982, W.L. Daniel [41] proved that each positive integer can
be written as the difference of two powerful numbers in infinitely many ways. Moreover, a few
years later, R.A. Mollin and P.G. Walsh [141] proved that each integer m 0 has infinitely many
representations as m = P Q, where P and Q are powerful numbers neither of them being a perfect
square.
Previous Page Next Page