268 Jean-Marie De Koninck
711 828 (= 22 · 34 · 133)
the smallest number n whose index of composition is 3 (namely λ(711828)
3.09307) and which is the sum of two co-prime 3-powerful numbers: here n =
711 828 =
193
+
893.
712 800
the tenth number n 1 such that φ(σ(n)) = n (see the number 128).
714 240 (= 29 · 32 · 5 · 31)
the seventh Erd˝ os-Nicolas number (see the number 2 016).
716 035
the fourth number n such that
n2
+ 2 is powerful: here
716
0352
+ 2 =
33
·
412
·
33612
(see the number 265).
720 720
the largest number n that is divisible by each of the numbers
n1/5,
namely
here the numbers 1, 2, 3, . . . , 14 (see N. Ozeki [157]);
the 11th colossally abundant number (see the number 55 440).
721 970
the smallest number n such that β(n) β(n + 1) . . . β(n + 9): here 146
927 1108 6091 10955 28884 90249 240662 360991 721979
(see the number 714).
729 551
the smallest prime number q such that

p≤q
p is divisible by 30 030 (= 2 · 3 ·
5 · 7 · 11 · 13): here this sum is equal to 20 488 357 890 (see the number 269).
729 752
the tenth number n such that φ(n)σ(n) is a fourth power: here
φ(729752)σ(729752) =
8404
(see the number 170).
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