Those Fascinating Numbers 361
211 111 322 112
the 33rd insolite number (see the number 111).
211 121 114 112
the
34th
insolite number (see the number 111).
215 523 459 072 (=
216
·
33
·
3492)
the 1 000 000th powerful number (see the number 3 136).
221 322 261 600
the 16th powerful number n such that n+1 is also powerful: here 221 322 261 600 =
25 · 35 · 52 · 112 · 972 and 221 322 261 601 = 74 · 96012 (see the number 288).
232 250 619 601 (=7 · 11 · 13 · 17 · 31 · 37 · 73 · 163)
the smallest Carmichael number which is the product of eight prime numbers
(see the number 41 041).
250 330 350 875 (=
53
·
112
·
194
· 127)
(possibly) the only number whose index of composition is 2.2 and which can
be written as the sum of two co-prime numbers whose index of composition is
6: indeed,
250 330 350 875 =
53
·
112
·
194
· 127 =
311
·
74
+
223
·
313,
where
λ(53
·
112
·
194
· 127) 2.225,
λ(311
·
74)
6.52594,
λ(223
·
313)
6.35898;
four other numbers
1013
with an index of composition 2 can be written
as the sum of two numbers whose index of
composition207
is 6: these are
607 323 321, 398 656 076 841, 44 496 177 152 and 1 625 169 742 057.
252 096 675 073
the 10 000 000 000th prime power, in fact here a prime number (see the number
419).
207One
can easily show that assuming the abc Conjecture, there can only be finitely many such
numbers.
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