270 Jean-Marie De Koninck
766 261
the first term of the smallest sequence of 11 consecutive prime numbers all of
the form 4n + 1 (see the number 2 593).
768 594
the fifth number n such that σ(n), σ(n + 1), σ(n + 2), σ(n + 3) and σ(n + 4)
all have the same prime factors, namely here the primes 2, 3, 5, 7 and 61 (see
the numbers 3 777 and 20 154).
783 700
the third multiple of 100 for which the next 100 numbers include exactly
17 prime numbers, namely 783701, 783703, 783707, 783719, 783721, 783733,
783737, 783743, 783749, 783763, 783767, 783779, 783781, 783787, 783791,
783793 and 783799 (see the number 400).
798 644
the tenth number which is not a palindrome, but whose square is a palindrome:
here 798 6442 = 637832238736 (see the number 26).
801 340
the smallest abundant number n such that n + 2, n + 4, n + 6, n + 8 and n + 10
are also abundant (see the number 348).
806 095
the number of Niven numbers
107
(see the number 213).
811 538
the smallest number which can be written as the sum of three distinct fourth
powers in three distinct ways:
811 538 =
44
+
234
+
274
=
74
+
214
+
284
=
124
+
174
+
294,
a representation first obtained in 1966 by Lander & Parkin [122] (see the num-
ber 6 578).
815 654
the
12th
number n such that φ(n)σ(n) is a fourth power: here
φ(815654)σ(815654) =
8404
(see the number 170).
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