308 Jean-Marie De Koninck
32 509 439
the tenth solution of σ2(n) = σ2(n + 2) (see the number 1 079).
32 535 999
the smallest number n such that n and n+1 each have 12 prime factors counting
their multiplicity: here 32 535 999 =
310
· 19 · 29 and 32 536 000 =
26
·
53
·
72
· 83
(see the number 135).
32 582 657
the exponent of the
44th
Mersenne prime
232 582 657−1
(a 9 808 358 digit number)
discovered by Curtis Cooper and Steven Boone on September 4, 2006, using
the programme developed by G. Woltman (see the number 1 398 269).
32 694 619
the smallest prime number q1 such that each number qi = 3qi−1 + 2 is prime
for i = 2, 3, . . . , 8 (see the number 575 119): such a sequence of prime numbers
is somewhat similar to the Cunningham chains (see the number 1 122 659).
33 550 336 (= 212(213 1))
the fifth perfect number (the smallest four are 6, 28, 496 and 8 128).
33 721 216
the
12th
dihedral perfect number (see the number 130).
33 757 004
the number n which allows the sum
m≤n
ω(m)=2
1
m
to exceed 6 (see the number 44).
34 012 224
the smallest number n 1 whose sum of digits is equal to
6

n: the only other
numbers n 1 satisfying this property are 8 303 765 625, 24 794 911 296 and
68 719 476 736;
the smallest number which can be written as the sum of three distinct cubes
in ten distinct ways:
34 012 224 =
363
+
2163
+
2883
=
393
+
1533
+
3123
=
413
+
1143
+
3193
=
453
+
2463
+
2673
=
723
+
1143
+
3183
=
1003
+
1923
+
2963
=
1023
+
2273
+
2773
=
1183
+
1863
+
2963
=
1623
+
2163
+
2703
=
1733
+
2143
+
2673
(see the number 1 009).
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