Those Fascinating Numbers 197
18 287
the smallest prime factor of the Mersenne number
2223
1, whose complete
factorization is given by
2223
1 = 18287 · 196687 · 1466449 · 2916841
·1469495262398780123809 · 596242599987116128415063;
it is the smallest Mersenne number with exactly six prime factors (see the num-
ber 223 for the list of the smallest numbers which require a given number of
distinct primes).
18 315
the 21rst solution of φ(n) = φ(n + 1) (see the number 15).
18 444
the smallest number n such that ω(n) + ω(n + 1) + ω(n + 2) + ω(n + 3) = 15:
here 18 444 = 22 · 3 · 29 · 53, 18 445 = 5 · 7 · 17 · 31, 18 446 = 2 · 23 · 401 and
18 447 = 3 · 11 · 13 · 43 (see the number 987).
18 486
the third composite number n (and the largest 109) which divides the ex-
pression σ(n) + φ(n) + γ(n) (see the number 198).
18 490
the third number n divisible by a square 1 and such that δ(n + 1) δ(n) = 1
(see the number 49).
18 496
the fifth number n 1 such that n · 2n + 1 is prime (see the number 141).
18 523
the 16th prime number pk such that p1p2 . . . pk + 1 is prime (see the number
379).
18 600
the eighth number which is not perfect or multi-perfect but whose harmonic
mean is an integer (see the number 140).
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