Those Fascinating Numbers 261
465 125 (= 53 · 612)
the smallest powerful number n such that n 1 is a perfect square (namely
6822):
the second number satisfying this property is
1 610 006 506 595 061 125 = 1 268 860
3182
+ 1 =
53
·
172
·
612
·
1094412
(see the number 682).
467 458
the third even number n such that σI (n) = σI (n + 2) (see the number 54 178).
470 449
the
13th
number n such that
n2
1 is powerful: here
470
4492
1 =
25
·
35
·
52
·
112
·
972
(see the number 485).
470 832
the eighth solution y of the Fermat-Pell equation x2 2y2 = 1: here (x, y) =
(665857, 470832); see the number 99.
472 601
the second composite number n such that σ(n+56) = σ(n)+56 (see the number
76 571).
480 441
the sixth number n such that φ(n)σ(n) is a fourth power: here
φ(480441)σ(480441) = 6724 (see the number 170).
480 852
the smallest number n such that π(n) = n/12 (see the number 330).
481 824
the
13th
number n such that σ(n) and σ2(n) have the same prime factors,
namely the primes 2, 3, 5, 7 and 13 (see the number 180).
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