Those Fascinating Numbers 237

109 376

• the smallest six digit automorphic number: 109

3762

= 11 963 109 376 (see the

number 76).

109 453

• the smallest number n such that P (n) P (n + 1) . . . P (n + 8): here

109453 54727 7297 6841 4759 2027 823 421 107 (see the

number 1 851).

109 989

• the fifth number which is not a palindrome, but which divides the number

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

110 487 (= 3 · 13 · 2833)

• the 100

000th

composite number (see the number 133).

110 503

• the exponent of the

29th

Mersenne prime

2110 503

− 1 (Colquitt and Welsch,

1988).

110 880

• the

25th

superabundant number: we say that n is superabundant if σ(n)/n

σ(m)/m for each number m n; the sequence of numbers satisfying this pro-

perty begins as follows: 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720,

840, 1 260, 1 680, 2 520, 5 040, 10 080, 15 120, 25 200, 27 720, 55 440, 110 880,

166 320, 277 200, 332 640, 554 400, 665 280, 720 720, 1 441 440, . . .

113 343

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

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

114 243

• the 12th number n such that n2 −1 is powerful: here 114 2432 −1 = 23 ·134·2392

(see the number 485).

114 688

• the 17th Granville number (see the number 126).