226 Jean-Marie De Koninck
74 848
the smallest number n such that
f(n + 1) = f(n + 2) = f(n + 3) = f(n + 4) = f(n + 5),
where f(n) stands for the product of the exponents in the factorization of n
(see the number 843).
75 239
the second prime number q such that

p≤q
p is a multiple of 1 000: the se-
quence of numbers satisfying this property begins as follows: 35 677, 75 239,
81 761, 85 199, 85 531, 86 813, 95 717, . . .
75 329
the smallest prime number p such that Ω(p 1) = Ω(p + 1) = 8: here 75 328 =
26
· 11 · 107 and 75 330 = 2 ·
35
· 5 · 31 (see the number 271).
75 361 (= 11 · 13 · 17 · 31)
the third pseudoprime in bases 2, 3, 5 and 7 (see the number 29 341).
76 544
the smallest number n such that 9! divides 1+2+ . . . + n (see the number 224);
the smallest number n such that n and n + 1 are both divisible by a seventh
power: 76 544 = 28 · 13 · 23 and 76 545 = 37 · 5 · 7 (see the number 1 215).
76 571
the smallest composite number n such that σ(n+56) = σ(n)+56; the composite
numbers 472 601, 929 964, 1 644 236, 3 143 591, 21 887 471 and 28 724 844 are also
solutions of this equation.
77 140
the smallest 5-composite number n such that n+2 is also a 5-composite number:
here 77 140 =
22
· 5 · 7 · 19 · 29 and 77 142 = 2 · 3 · 13 · 23 · 43 (see the number
1 428).
77 141
the smallest prime number p such that p 1 and p + 1 each have exactly five
distinct prime factors: here 77 140 =
22
·5·7·19·29 and 77 142 = 2·3·13·23·43
(see the number 131).
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