96 Jean-Marie De Koninck
607
the exponent of the 14th Mersenne prime 2607 1 (Robinson, 1952).
608
the fifth number n such that the corresponding triangular number Tn =
n(n+1)
2
is the product of three consecutive numbers: here
608 · 609
2
= 56 · 57 · 58; there
exist only six triangular numbers satisfying this property, namely T3, T15, T20,
T44, T608 and T22736 (N. Tzanahis & B.M.M. de Weger [197]).
609
the smallest solution of
φ(n)
n
=
16
29
; the sequence of numbers satisfying this
equation begins as follows: 609, 1827, 4263, 5481, 12789, 16443, 17661, 29841,. . .
610
the
12th
Markoff number (see the number 433).
613
the rank of the 23rd Lucas prime number: a Lucas number is a member of the
recurrence sequence (
n
)n≥1 defined by
1
= 1,
2
= 3 and
n+1
=
n
+
n−1
for each integer n 2; the prime numbers belonging to this sequence are called
Lucas prime numbers; the only known numbers n such that
n
is prime are: 2,
4, 5, 7, 8, 11, 13, 16, 17, 19, 31, 37, 41, 47, 53, 61, 71, 79, 113, 313, 353, 503,
613, 617, 863, 1097, 1361, 4787, 4793, 5851, 7741, 8467, 10691, 12251, 13963,
14449, 19469, 35449, 36779, 44507 and 51169.
616
the smallest number n which allows the sum
i≤n
1
i
to exceed 7 (see the number
83).
617
the number of digits in the decimal expansion of the Fermat number
2211
+ 1.
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