Those Fascinating Numbers 221
50 811
the smallest number n which allows the sum
m≤n
1
φ(m)
to exceed 21 (see the
number 177).
51 169
the
41rst
(and largest known) Lucas prime number (see the number 613).
51 301 (=
292
· 61)
the smallest (and possibly the only) 19-hyperperfect number.
51 984
the
11th
powerful number which can be written as the sum of two co-prime
3-powerful numbers = 1: 51 984 = 1 331+50 653, that is
24
·
32
·
192
=
113 +373
(see the number 841).
52 020
the sixth number n such that σ(n) and σ2(n) have the same prime factors,
namely the primes 2, 3, 7, 13 and 307 (see the number 180).
52 488
the
100th
3-powerful number (see the number 216).
54 178
the smallest even number n such that σI (n) = σI (n + 2); the sequence of
numbers satisfying this property begins as follows: 54 178, 230 578, 467 458,
5 058 180, 5 761 978, 28 119 418, 34 385 818, 35 080 502, 37 387 980, . . .
54 748
the fourth number which can be written as the sum of the fifth powers of its
digits: 54 748 = 55 + 45 + 75 + 45 + 85 (see the number 4 150).
55 296
the sixth number n 2 such that
σ(n) + φ(n)
γ(n)2
is an integer (see the number
588).
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