306 Jean-Marie De Koninck
25 417 732
the smallest number 1 which is equal to the sum of the squares of the
factorials of its digits in base 8: here 25 417 732 = [1, 4, 0, 7, 5, 4, 0, 0, 4]8 =
1!2 +4!2 +0!2 +7!2 +5!2 +4!2 +0!2 +0!2 +4!2 (see the numbers 145 and 40 585).
25 430 981
the second number 1 which is equal to the sum of the squares of the factorials
of its digits in base 8: here 25 430 981 = [1, 4, 1, 0, 0, 5, 7, 0, 5]8 = 1!2 +4!2 +1!2 +
0!2
+
0!2
+
5!2
+
7!2
+
0!2
+
5!2
(see the number 25 417 732).
25 457 760
the eighth number n such that β(n)|β(n+1) and β(n+1)|β(n+2): here 164|984
and 984|1157184 (see the number 225 504).
25 658 441
the first component p of the third 8-tuple (p, p +2, p +6, p +8, p +12, p +18, p +
20, p + 26) made up entirely of prime numbers: the smallest such 8-tuple is
(11, 13, 17, 19, 23, 29, 31, 37), while the second is the one whose first component
is 15 760 091.
25 741 470
the fourth solution of σ(n) = σ(n + 15) (see the number 26).
25 964 951
the exponent of the
42nd
Mersenne prime
225 964 951
1 (a 7 816 230 digit num-
ber) discovered by Martin Nowak (an eye surgeon) on February 18, 2005, using
the programme developed by G. Woltman (see the number 1 398 269).
26 888 999
the smallest number of persistence 9 (see the number 679).
26 890 623
the first of the smallest three consecutive numbers each divisible by a sixth
power: 26 890 623 = 36 ·36887, 26 890 624 = 27 ·19·11057, 26 890 625 = 56 ·1721
(see the number 1 375).
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