Those Fascinating Numbers 253
290 783
the smallest number n such that P (n + i)

n + i for i = 0, 1, 2, 3, 4, 5, 6; the
largest prime factors of these seven are respectively 271, 233, 311, 419,
227, 523 and 269, all smaller than
√numbers
290783 539; it is also the smallest number
n such that P (n + i)

n + i for i = 0, 1, 2, 3, 4, 5, 6, 7, since P (290790) = 359
(see the numbers 1 518 and 134 848).
293 760 (=
27
·
33
· 5 · 17)
the smallest solution of
σ(n)
n
=
15
4
; the sequence of numbers satisfying this
equation begins as follows: 293 760, 1 782 144, 3 485 664, 282 977 280,
1 716 728 832,. . .
294 001
the smallest prime number such that if one replaces any of its digits by any
another digit, one obtains a composite number.
297 864
the smallest Niven number n such that n +60 is also a Niven number, but with
no others in between (see the number 28 680).
301 140
the 11th number n such that σ(n) and σ2(n) have the same prime factors,
namely the primes 2, 3, 5, 7 and 13 (see the number 180).
310 154
the smallest number n such that ω(n) + ω(n + 1) + ω(n + 2) = 14: here
310 154 = 2·13·79·151, 310 155 = 3·5·23·29·31 and 310 156 = 22 ·7·11·19·53
(see the number 2 210).
319 489
the smallest prime factor of the Fermat number F11 =
2211
+1, whose complete
factorization is given by
F11 = 319489·974849·167988556341760475137·3560841906445833920513·P564.
322 033 (= 251 · 1283)
the 100
000th
number having exactly two distinct prime factors (see the number
184).
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