Those Fascinating Numbers 269
730 753
the smallest prime factor of the Mersenne number
2173
1, whose complete
factorization is given by
2173
1 = 730753 · 1505447 · 70084436712553223 · 155285743288572277679887.
742 900
the
13th
Catalan number (see the number 14).
751 530
the second number n 1 such that the sum of the divisors of its cube is a
perfect square:
σ(7515303)
=
12920544002;
the smallest number n 1 with
this property is n = 7:
σ(73)
=
202
(Fermat, 1657).
752 694 (= 2 · 3 · 331 · 379)
the smallest number n which allows the sum
m≤n
ω(m)=4
1
m
to exceed 1 (see the
number 45 848 700).
755 968
the first of the nine smallest consecutive numbers where the Ω(n) function takes
on different values, namely here the values 9, 1, 5, 2, 7, 8, 3, 4 and 6 (see the
number 726).
755 972
the
11th
number n such that φ(n)σ(n) is a fourth power: here
φ(755972)σ(755972) =
8404
(see the number 170).
756 839
the exponent of the
32nd
Mersenne prime
2756 839
1 (Slowinski, 1992).
764 392
the fourth number n such that σ(n), σ(n + 1), σ(n + 2), σ(n + 3) and σ(n + 4)
all have the same prime factors, namely here 2, 3, 5, 7 and 13: indeed,
σ(n) = 2 ·
32
·
53
·
72
· 13,
σ(n + 1) =
27
· 3 ·
52
· 7 · 13,
σ(n + 2) =
25
· 3 ·
52
·
72
· 13,
σ(n + 3) =
25
·
32
· 5 ·
72
· 13,
σ(n + 4) =
22
· 3 ·
52
·
73
· 13;
see the numbers 3 777 and 20 154.
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