Those Fascinating Numbers 139
1 907
the
12th
number n for which the distance from
en
to the nearest integer is the
smallest (see the number 178).
1 909 (= 23 · 83)
the second 18-hyperperfect number (see the number 1 333).
1 919
the smallest number n 1 such that σ(n + 1) = 3σ(n): the only numbers
n 107 satisfying this equation are 1 919, 2 759, 11 219, 27 089, 50 039, 58 463,
100 127, 113 831, 115 289, 120 203, 131 879, 148 511, 233 729, 244 319, 308 039,
461 099, 554 063, 596 447, 1 406 303, 1 486 619, 2 285 519, 2 880 989, 5 138 783,
5 369 111, 5 521 619, 5 736 743, 6 621 383, 7 496 279, 7 683 191, 8 571 527, 8 848 619
and 9 563 231 (see the numbers 206, 1 253 and 37 033 919).
1 924
the second number whose square can be written as the sum of three fourth
powers:
19242
=
244
+
304
+
404
(see the number 481).
1 934
the smallest number n such that the Liouville function λ0 takes successively,
starting with n, ten times in a row the value 1 (as well, in this case, as 11 and 12
times in a row); denoting by nk the smallest number n such that λ0(n + i) = 1
for i = 0, 1, 2, . . . , k 1, we have the following table:
k nk
1 1
2 9
3 14
4 33
5 54
6 140
7 140
8 213
9 213
10 1 934
k nk
11 1 934
12 1 934
13 35 811
14 38 405
15 38 405
16 200 938
17 200 938
18 389 409
19 1 792 209
20 5 606 457
k nk
21 8 405 437
22 8 405 437
23 8 405 437
24 8 405 437
25 68 780 189
26 68 780 189
27 68 780 189
28 68 780 189
29 880 346 227
30 880 346 227
(see the number 5 879 for the list of the smallest numbers nk such that λ0(nk +
i) = −1 for i = 0, 1, 2, . . . , k 1).
Previous Page Next Page