208 Jean-Marie De Koninck
29 341
the smallest pseudoprime in bases 2, 3, 5 and 7; it is also the smallest pseudo-
prime in bases 2, 3, 5, 7 and 11; the sequence of pseudoprimes in bases 2, 3, 5
and 7 begins as follows: 29341, 46657, 75361, 115921, 162401, . . .
29 355
the eighth number such that 2n + n2 is prime (see the number 2 007).
29 395
the second number n such that σ(n), σ(n + 1), σ(n + 2), σ(n + 3) and σ(n + 4)
have the same prime factors, namely here 2, 3, 5 and 7 (see the numbers 3 777
and 20 154).
29 888
the smallest number n such that n and n + 1 each have seven prime factors
counting their multiplicity: 29 888 =
26
· 467 and 29 889 =
36
· 41 (see the
number 135).
30 031
the smallest number of the form p1p2 . . . pk +1 which is not prime: here 30 031 =
2 · 3 · 5 · 7 · 11 · 13 + 1 = 59 · 509.
30 240
the smallest 4-perfect number, that is a number n such that σ(n) = 4n; the
list of 4-perfect numbers begins as follows: 30 240, 32 760, 2 178 540, 23 569 920,
45 532 800, 142 990 848, 1 379 454 720, 43 861 478 400, 66 433 720 320,
153 003 540 480, 403 031 236 608, . . . ; there seems to exist only 36 4-perfect num-
bers (see R.K. Guy [101], B2).
30 375
the smallest number n which allows the sum
m≤n
1
φ(m)
to exceed 20 (see the
number 177).
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