250 Jean-Marie De Koninck
228 727
the third composite number n such that
2n−2
1 (mod n); see the number
20 737.
229 999
the largest number n such that f5(n) n, where f5(n) = f([d1, d2, . . . , dr]) =
d1
5
+ d2
5
+ . . . + dr
5,
where d1, d2, . . . , dr stand for the digits of n.
230 387
the smallest number n such that π(n)
n
log n
+
n
log2
n
+
2n
log3
n
+
6n
log4
n
, this
last expression representing the first four terms of the asymptotic expansion of
Li(n): here we have π(230387) = 20474 while
n
log n
+
n
log2
n
+
2n
log3
n
+
6n
log4
n
n=230387
20473.9 (see the number 73).
230 578
the second even number n such that σI (n) = σI (n+2) (see the number 54 178).
230 769
the sixth number which quadruples when its last digit is moved in first position
(see the number 102 564).
234 256 (=
224)
the second number n 1 whose sum of digits is equal to
4

n (see the number
2 401).
234 613
the smallest number n such that τ (n) τ (n + 1) . . . τ (n + 8): here
4 4 8 8 8 8 12 12 12 (see the number 241).
235 224
the sixth powerful number n such that n + 1 is also powerful (see the number
288): here 235 224 = 23 · 35 · 112 and 235 225 = 52 · 972.
241 603
the first term of the smallest sequence of 11 consecutive prime numbers all of
the form 4n + 3 (as well as 12 or 13 consecutive prime numbers all of the form
4n + 3); see the number 463.
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