368 Jean-Marie De Koninck

5 209 105 541 772

• the sixth number which is not the square of a prime number, but which can be

written as the sum of the squares of some of its prime factors: indeed,

5 209 105 541 772 =

22

· 3 · 11 · 17291 · 2282281 =

32

+

112

+

172912

+

22822812

(see the number 870).

5 737 850 066 077

• the median value of the fourth prime factor of an integer (see the number 37);

this value was obtained by David Gr´ egoire using an algorithm programmed in

C language.

5 832 742 205 057

• the

19th

Bell number (see the number 52).

6 722 988 818 432

• the largest number n whose sum of digits is equal to

7

√

n (see the number

612 220 032).

6 963 472 309 248

• the smallest number which can be written as the sum of two cubes in four

distinct ways:

6 963 472 309 248 =

24213

+

190833

=

54363

+

189483

=

102003

+

180723

=

133223

+

166303

(E. Rosenstiel, J.A. Dardis & C.R. Rosenstiel [177]); see the number 1 729.

7 432 339 208 719

• the smallest prime factor of the Mersenne number 2101 − 1, whose complete

factorization is given by

2101

− 1 = 7 432 339 208 719 · 341 117 531 003 194 129.

8 192 480 787 000

• the 19th powerful number n such that n + 1 is also powerful: here

8 192 480 787 000 =

23

·

32

·

53

·

433

·

1072

and 8 192 480 787 001 =

72

·

412

·

99732

(see the number 288).

8 992 165 119 733

• an 18-hyperperfect number, possibly the fifth one (see the number 1 333).