Those Fascinating Numbers 307

27 412 679

• the number of twin prime pairs 1010 (see the number 1 224).

27 644 437

• the 13th Bell number (see the number 52).

28 119 418

• the sixth even number n such that σI (n) = σI (n + 2) (see the number 54 178).

28 600 321 (= 312 · 29761)

• the second 30-hyperperfect number (see the number 3 901).

29 149 139

• the smallest number n for which the Moebius function µ takes on successively,

starting with n, the values 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0 (see the number 3 647).

30 002 960

• the 17th number n such that φ(n) + σ(n) = 3n (see the number 312).

30 042 907

• the largest known number whose square is the sum of a cube and an eighth

power: here 30 042 9072 = 96 2223 + 438 (see the number 122).

30 402 457

• the exponent of the 43rd Mersenne prime 230 402 457 − 1 (a 9 152 052 digit num-

ber) discovered by Curtis Cooper and Steven Boone on December 15, 2005,

using the programme developed by G. Woltman (see the number 1 398 269).

30 459 361 (= 55192)

• the smallest powerful number n such that n +14 is also powerful: here n +14 =

33

·

55

·

192;

the sequence of numbers satisfying this property begins as follows:

30 459 361, 717 498 661, 1 090 122 275, 185 344 887 289,. . .

192.

192This sequence is infinite (see the number 214 369).