Those Fascinating Numbers 143

2 137

• the smallest number n requiring nine iterations of the σI (n) function in order

to reach 1 (see the number 193).

2 158

• the second solution of σ2(n) = σ2(n + 4) (see the number 430).

2 176 (=

27

· 17)

• the 14th unitary hyperperfect number (see the number 288).

2 178

• the second number which is not a palindrome but which divides the number

obtained by reversing its digits (see the number 1 089).

2 184

• the smallest 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 (R.K. Guy [101], B28,

with an obvious error in the formulation): the sequence of numbers satisfying

this property begins as follows: 2 184, 27 830, 32 214, 57 860, 62 244, 87 890,

92 274, . . .

2 187

• possibly the largest 3-powerful number which is the nearest (a distance of 10) to

the following 3-powerful number, namely 2197: here 2 187 =

37

and 2 197 =

133;

the next relatively small gap (this one being equal to 28) occurs with the

numbers 50 625 =

34

·

54

and 50 653 =

273.

2 203

• the exponent of the 16th Mersenne prime 22 203 − 1 (Robinson, 1952).

2 204

• the

11th

solution of φ(n) = φ(n + 1) (see the number 15).

2 205

• the third of the existing eight primitive non deficient numbers (see the number

945).