134 Jean-Marie De Koninck
1 674
the smallest number n which allows the sum
i≤n
1
i
to exceed 8 (see the number
83).
1 675
the third number which does not produce a palindrome by the 196-algorithm
(see the number 196).
1 676
the seventh number n 9 such that n =
∑r
i=1
di,
i
where d1, . . . , dr stand for
the digits of n: here 1 676 =
11
+
62
+
73
+
64
(see the number 175).
1 680 (=
24
· 3 · 5 · 7)
the 17th highly composite number (see the number 180).
1 681 (= 412)
the smallest composite number of the form
n2
+ n + 41 (with n = 40);
the smallest composite number of the form
n2
79n + 1601 (with n = 80);
the smallest solution of γ(n + 1) γ(n) = 17: the only solutions n
109
are
1 681, 59 535, 139 239 and 505 925 (see the footnote tied to the number 98);
the second number n divisible by a square 1 and such that δ(n+1)−δ(n) = 1
(see the number 49);
the fourth solution w + s of the aligned houses problem (see the number 35).
1 682
the fifth number n such that the binomial coefficient
(
n
2
)
is a perfect square:
here
(1682)
2
=
11892
(see the number 289).
1 701 (=
35
· 7)
the second number n divisible by a square 1 and such that γ(n+14) = γ(n)+
14: the smallest is 49 (and there are no others 108); here γ(n + 14) γ(n) =
γ(1715) γ(1701) = γ(73 · 5) γ(35 · 7) = 35 21 = 14.
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