Those Fascinating Numbers 207
27 830
the second number n such that each of the numbers n+i, i = 0, 1, 2, . . . , 16, has
a factor in common with the product of the other 16 (see the number 2 184).
27 846
the tenth number which is not perfect or multi-perfect but whose harmonic
mean is an integer (see the number 140).
28 032
the smallest number n such that P (n + i)

n + i for i = 0, 1, 2, 3, 4, 5; the
largest prime factors of these six numbers are respectively 73, 97, 131, 89, 163
and 53, and thus all smaller than

28 032 167 (see the number 1 518).
28 374
the smallest number n such that τ (n) = τ (n + 1) = τ (n + 2) = τ (n + 3) =
τ (n + 4) = τ (n + 5): the sequence of numbers satisfying this property begins as
follows: 28 374, 90 181, 157 493, 171 893, 171 894, 180 965, 180 966, . . . (see the
number 33).
28 657
the eighth prime Fibonacci number (see the number 89).
28 680
the smallest Niven number n such that n +30 is also a Niven number, but with
no others in between; if nk, for k 2, stands for the smallest Niven number n
such that n + k is also a Niven number, but with no others in between, then
n10 = 90, n20 = 7 560, n30 = 28 680, n40 = 119 772, n50 = 154 876, n60 =
297 864, n70 = 968 760, n80 = 7 989 168, n90 = 2 879 865 and n100 = 87 699 842.
28 721
the ninth number whose square can be written as the sum of three fourth
powers: 28
7212
=
604
+
1354
+
1484
(see the number 481).
28 974
the smallest number n such that τ (n) τ (n + 1) . . . τ (n + 4); it is also
the smallest number n such that τ (n) τ (n + 1) . . . τ (n + 5): here
16 12 10 8 4 2 (see the number 45).
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