Those Fascinating Numbers 313

45 841 247

• the 12th solution of σ2(n) = σ2(n + 2) (see the number 1 079).

45 848 700 (= 22 · 32 · 52 · 16981)

• the number n which allows the sum

m≤n

ω(m)=4

1

m

to exceed 2 (see the number

752 694).

46 248 900

• the sixth number n such that σ3(n) is a perfect square: here σ3(46248900) =

3434567293922 (see the number 345).

46 908 264

• the smallest integer n such that ω(n), ω(n + 1), . . . , ω(n + 6) are all distinct,

namely in this case with the values 6, 3, 2, 5, 4, 1 and 7 (see the number 417).

47 326 700

• the smallest multiple of 100 which is followed by at least 200 consecutive com-

posite numbers.

47 639 670 (= 2 · 3 · 5 · 13 · 23 · 47 · 113)

• the

11th

ideal number (see the number 390).

47 775 744

• the sixth number which is equal to the product of the factorials of its digits in

base 5: 47 775 744 = [4, 4, 2, 1, 2, 3, 1, 0, 4, 3, 4]5 = 4!·4!·2!·1!·2!·3!·1!·0!·4!·3!·4!

(see the number 144).

48 024 900

• the sixth number which is both a triangular number and a perfect square:

48 024 900 =

9800(9800+1)

2

=

69302

(see the number 36).

49 436 927

• the

13th

solution of σ2(n) = σ2(n + 2) (see the number 1 079).