Those Fascinating Numbers 355
38 358 837 677
the smallest known prime number p for which inequality
π2(p)
ep
log p
π
p
e
does not hold; Ramanujan proved that this inequality holds for p sufficiently
large (see B.C. Berndt [21], as well as the number 2 418).
43 861 478 400 (=
210
·
33
·
52
· 23 · 31 · 89)
the eighth 4-perfect number (see the number 30 240).
44 496 177 152
the smallest number with an index of composition 2 which can be written as
the sum of two co-prime numbers each with an index of composition 7: we
have
44 496 177 152 =
211
·
74
· 9049 =
198
+
317,
where
λ(211
·
74
· 9049) 2.08679,
λ(198)
= 8,
λ(317)
= 7
(see the number 607 323 321).
51 001 180 160
(=214
· 5 · 7 · 19 · 31 · 151)
the sixth tri-perfect number and the largest one known (see the number 120).
52 523 350 144 (=
347)
the fourth number n 1 whose sum of digits is equal to
7

n (see the number
612 220 032).
55 420 693 056
the seventh number which is both triangular and a perfect square: 55 420 693 056 =
332928(332928+1)
2
= 2354162 (see the number 36).
61 917 364 224
the smallest fifth power which can be written as the sum of four fifth powers:
61 917 364 224 =
1445
=
275
+
845
+
1105
+
1335
(Lander & Parkin [122]).
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