Those Fascinating Numbers 285
2 999 999
the largest number n such that f6(n) n, where f6(n) = f6([d1, d2, . . . , dr]) =
d1 6 + d2 6 + . . . + dr 6, where d1, d2, . . . , dr stand for the digits of n.
3 020 626
the fourth even number n such that
2n
2 (mod n); see the number 161 038.
3 021 377
the exponent of the 37th Mersenne prime 23 021 377 −1 discovered by R. Clarkson
(a 19 year old student) in 1998 using the programme developed by G. Woltman
(see the number 1 398 269).
3 263 443
the sixth voracious number (see the number 1 807).
3 290 624
the smallest number n such that n and n + 1 each have ten prime factors
(counting their multiplicity); indeed, 3 290 624 = 29 · 6427 and 3 290 625 =
34 · 55 · 13 (see the number 135).
3 343 776
the
11th
number n such that φ(n) + σ(n) = 3n (see the number 312).
3 345 408
the 13th number n 1 such that φ(σ(n)) = n (see the number 128).
3 358 169
the first term of the smallest sequence of 12 consecutive prime numbers all of
the form 4n + 1 (see the number 2 593).
3 370 501
the sixth and largest solution x of the Bachet equation x2 + 999 = y3 (see the
number 251).
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