272 Jean-Marie De Koninck

884 730

• the third and largest solution n 109 of σ(n) = 3n + 18 (see the number

17 850).

885 735 (= 311 · 5)

• the third number n having at least two distinct prime factors and such that

β(n)3|B1(n): here (3 + 5)3|(311 + 5) (see the number 5 120).

890 625

• the largest six digit automorphic number: here 890 6252 = 793212890625 (see

the number 76).

917 280

• the largest number n = [d1, . . . , dr] such that (d1 + r) · . . . · (dr + r) = n; the

numbers satisfying this property are: 12, 24, 35, 56, 4 752, 7 744, 16 500, 91 728

and 917 280; this is an observation due to Patrick Letendre.

917 504

• the

20th

Granville number (see the number 126).

925 957

• the seventh self contained number (see the number 293).

929 964

• the third composite number n such that σ(n +56) = σ(n)+56 (see the number

76 571).

930 249

• the

15th

number n such that

n2

− 1 is powerful; here

930

2492

− 1 =

24

·

53

·

112

·

312

·

612

(see the number 485).

944 108

• the third number n such that β(n)|β(n +1) and β(n +1)|β(n +2): here 555|555

and 555|4995 (see the number 225 504).