Those Fascinating Numbers 277
1 221 858
the smallest number having more than three distinct prime factors and which
is divisible by the cube of the sum of its prime factors: the sequence of num-
bers satisfying this property begins as follows: 1 221 858, 2 406 250, 2 443 716,
2 457 000, 3 346 110, 3 622 080, 3 665 574, . . . (see the number 37 026).
1 257 787
the exponent of the
34th
Mersenne prime
21 257 787
1 (Slowinski, 1996).
1 258 500
the smallest number n such that P (n + i)

n + i for i = 0, 1, 2, 3, 4, 5, 6, 7,
8; the largest prime factors of these nine numbers are respectively 31, 23, 251,
971, 599, 857, 179, 367 and 1117, all smaller than

1258500 1121 (see the
number 1 518).
1 294 298
the smallest number n such that P
(n)2|n,
P (n +
1)2|n
+ 1 and P (n +
2)2|n
+ 2:
here we have 1 292 298 = 2 · 61 · 1032, 1 292 299 = 34 · 19 · 292 and 1 292 300 =
22 ·52 ·7·432; the sequence of numbers satisfying this property begins as follows:
1 294 298, 9 841 094, 158 385 500, 1 947 793 550, . . .
1 295 953
the 100
000th
prime power, in fact here a prime number (see the number 419).
1 296 378
the smallest number which can be written as the sum of three distinct cubes
in six distinct ways:
1 296 378 =
33
+
763
+
953
=
93
+
333
+
1083
=
213
+
773
+
943
=
313
+
593
+
1023
=
333
+
813
+
903
=
603
+
753
+
873
(see the number 1 009).
1 299 709
the 100 000th prime number (see the number 541).
1 304 498
the smallest number n such that π(n) = n/13 (see the number 330).
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