346 Jean-Marie De Koninck
4 294 967 295
the largest known number n such that σ(φ(n)) = γ(n); the known numbers
satisfying this equation are
3 = 3,
15 = 3 · 5,
255 = 3 · 5 · 17,
2 418 = 2 · 3 · 13 · 31,
65 535 = 3 · 5 · 17 · 257,
110 771 178 = 2 · 3 · 7 · 19 · 127 · 1093,
4 294 967 295 = 3 · 5 · 17 · 257 · 65537
(see also the number 744).
4 294 967 297 (=
225
+ 1 = 641 · 6 700 417)
the sixth Fermat number, and the smallest composite one.
4 428 914 688 (= 213 · 32 · 11 · 43 · 127)
the fourth solution of
σ(n)
n
=
13
4
(see the number 360).
4 473 671 462
the fourth number which can be written as the sum of the cubes of its prime
factors:
4 473 671 462 = 2 · 13 · 179 · 593 · 1621 =
23
+
133
+
1793
+
5933
+
16213
(see the number 378).
4 679 307 774
the smallest number which is equal to the sum of the tenth powers of its digits.
4 700 063 497 (= 19 · 47 · 5 263 229)
the smallest solution of
2n
3 (mod n) (see R.K. Guy [101], F10).
4 758 958 741
the smallest prime number p such that p + 300 is prime and such that each
number between p and p + 300 is composite (see the number 396 733).
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