Those Fascinating Numbers 311
39 916 800
the value of 11! .
39 916 801
the smallest number n such that φ(n) = 11! (see the number 779).
40 373 802
the smallest number which is not a ninth power, but which can be written as
the sum of the ninth powers of some of its prime factors: here 40 373 802 =
2 · 34 · 7 · 35603 = 29 + 39 + 79 (see the number 870); most likely, there exist
infinitely many numbers satisfying this property: here are some of these:
10644853492 =
22
·
72
· 13 · 4177729 =
29
+
79
+
139,
322728051898 = 2 · 7 · 19 · 1213263353 =
29
+
79
+
199,
325045665153 =
33
· 11 · 19 · 57601571 =
39
+
119
+
199,
129972344294962 = 2 · 13 ·
372
· 503 · 7259491 =
29
+
139
+
379,
529032234098026 = 2 · 31 · 43 · 151 · 1314150311
=
29
+
319
+
439,
3571518874033609625764 =
22
· 11 · 211 · 241 · 25643 · 62248937467
=
29
+
2119
+
2419,
1393221691728239771756116 =
22
· 11 · 421 · 463 · 2309 · 2803 · 138181 · 181639
=
29
+
4219
+
4639,
7088956614339217590756132 =
22
·
33
· 223 · 283 · 577 · 47143 · 51803 · 738107
=
29
+
39
+
5779,
81640349467513249629369700 =
22
·
52
· 29 · 271 · 757 · 137227669154167919
=
29
+
2719
+
7579,
49578494676262451378580166876 =
22
· 181 · 1481 · 1543 · 601187 · 49845298913719
=
29
+
1819
+
15439.
40 575 616
the
13th
dihedral perfect number (see the number 130).
42 314 023 (= 1013 · 41771)
the 10 000
000th
number having exactly two distinct prime factors (see the num-
ber 184).
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