Those Fascinating Numbers 339
1 303 324 906
the smallest number n such that β(n) β(n + 1) . . . β(n + 11): here
1198 3190 5844 91691 753547 766221 4287274 118484094
217220824 260664988 325831231 434441642 (see the number 714).
1 375 298 099
the smallest number which can be written as a sum of three distinct fifth powers
in two distinct ways: 1 375 298 099 =
245
+
285
+
675
=
35
+
545
+
625
(for the
sum of fourth powers, see the number 2 673; for the sum of distinct fourth
powers, see the number 5 978 883; see also the number 6 578).
1 379 454 720 (= 28 · 3 · 5 · 7 · 19 · 37 · 73)
the seventh 4-perfect number (see the number 30 240): this number can be
obtained using the tri-perfect number 459 818 240 by observing that if n is
tri-perfect and (n, 3) = 1, then 3n is 4-perfect.
1 382 958 545
the 15th Bell number (see the number 52).
1 419 138 368
the second number which can be written as the sum of the fifth powers of three
numbers in two distinct ways:
1 419 138 368 =
135
+
515
+
645
=
185
+
445
+
665
(see the number 1 375 298 099).
1 433 272 320
the fourth number which is equal to the product of the factorials of its digits in
base 7: 1 433 272 320= [5, 0, 3, 4, 2, 4, 2, 0, 3, 3, 4]7 = 5!·0!·3!·4!·2!·4!·2!·0!·3!·3!·4!
(see the number 248 832 000).
1 459 956 960 (=
25
·
34
· 5 ·
72
·
112
· 19)
the second solution of
σ(n)
n
=
19
4
(see the number 746 444 160).
1 476 304 896 (=
213
· 3 · 11 · 43 · 127)
the fifth tri-perfect number (see the number 120): Carmichael proved that it is
the only tri-perfect number with exactly five distinct prime factors.
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