384 Jean-Marie De Koninck
13 744 803 133 596 058 624 (= 8210)
the smallest number n 1 whose sum of digits is equal to
10

n: the only other
numbers satisfying this property are 19 687 440 434 072 265 625,
53 861 511 409 489 970 176, 73 742 412 689 492 826 049,
179 084 769 654 285 362 176 and 480 682 838 924 478 847 449.
15 407 021 574 586 368 000
the fifth number which is equal to the product of the factorials of its digits in
base 7:
15 407 021 574 586 368 000 = [3, 6, 4, 0, 4, 2, 4, 0, 3, 3, 0, 3, 2, 4, 1, 6, 0, 3, 2, 2, 6, 1, 1]7
(see the number 248 832 000).
18 446 744 073 709 551 617
the smallest composite Fermat number; its factorization is
226
+ 1 = 18 446 744 073 709 551 617 = 274177 · 67280421310721.
19 687 440 434 072 265 625 (= 8510)
the second number n 1 whose sum of digits is equal to
10

n (see the number
13 744 803 133 596 058 624).
19 698 744 770 118 549 504 (=
253
·
37)
perhaps the smallest number n such that γ(n)4|σ(n) (see the number 96).
21 127 269 486 018 731 928
the number of prime numbers 1021.
32 032 215 596 496 435 569
the smallest prime factor of the Mersenne number 2137 1, whose complete
factorization is given by
2137
1 = 32032215596496435569 · 5439042183600204290159.
43 252 003 274 489 856 000 (=
8!·12!·38·212
2·2·3
)
the number of possible permutations of the Rubik cube (3 × 3 × 3), a result
obtained by E.C. Turner & K.F. Gold [196].
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