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).