394 Jean-Marie De Koninck
962 493 562 543 459 590 626 671 870 630 428 672 000 000 000 000
the seventh number which is equal to the product of the factorials of its digits
in base 12:
962 493 562 543 459 590 626 671 870 630 428 672 000 000 000 000
= [3, 1, 10, 9, 1, 11, 1, 8, 11, 7, 6, 1, 5, 3, 9, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]12 (see the number 21 772 800).
12 864 938 683 278 671 740 537 145 998 360 961 546 653 259 485 195 807
the ninth voracious number (see the number 1 807).
191 561 942 608 236 107 294 793 378 084 303 638 130 997 321 548 169 216
(=
288(289
1))
the tenth perfect number.
27 418 521 963 671 501 273 905 190 135 082 692 041 730 405 303 870 249
023 209
(=
39
·
73
·
113
·
133
·
173
·
413
·
433
·
473
·
4433
·
4993
·
35833)
the smallest cube whose sum of divisors is also a cube (Rubin):
σ(27418521963671501273905190135082692041730405303870249023209)
= 65400948817364742403487616930512213536407552000000000000000
=
402897602435328000003.
45 883 517 654 351 824 863 158 584 663 538 863 253 527 461 888 000 000
000 000 000
the eighth number which is equal to the product of the factorials of its digits
in base 12:
45 883 517 654 351 824 863 158 584 663 538 863 253 527 461 888 000 000 000 000 000
= [1, 4, 10, 7, 5, 8, 1, 0, 4, 6, 7, 0, 7, 3, 8, 7, 11, 8, 3, 4, 3, 6, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]12
(see the number 21 772 800).
210 913 096 528 905 026 899 530 575 850 386 805 453 832 507 856 329 770
499 303 938
(= 2 · 3 · 7 · 11 · 17 · 19 · 37 · 243871 · 61732369
·2537372468554462665091597215251362804089751)
the largest known number which is not an eighth power, but which can be
written as the sum of the eighth powers of some of its prime factors: indeed,
210913096528905026899530575850386805453832507856329770499303938
=
28
+
178
+
617323698
(see the number 870).
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