316 Jean-Marie De Koninck
71 265 503
the second number n such that φ(n), φ(n + 1), φ(n + 2), φ(n + 3), φ(n + 4) and
φ(n + 5) have the same prime factors, namely here the primes 2, 3, 5, 7 and
101 (see the number 43 570 803).
71 315 748
the eighth number n such that σ3(n) is a perfect square: indeed,
σ3(71315748) =
6564899577602
(see the number 345).
73 939 133
the largest known right truncatable prime number: such a number has the
property that, regardless the number of digits we remove from the right, the
remaining number is still prime: thus 7393913, 739391, 73939, 7393, 739,
73 and 7 are all primes; such a number is also sometimes called a super-
prime number (see I.O. Angell & H.J. Godwin [4], and see also the number
357 686 312 646 216 567 629 137 for the largest known left truncatable prime
number).
75 007 400
the
19th
number n such that φ(n) + σ(n) = 3n (see the number 312).
78 312 721
the smallest number n such that τ (n) τ (n + 1) . . . τ (n + 10): here
8 8 8 12 12 12 16 16 16 16 16 (see the number 241).
78 436 511
the
14th
solution of σ2(n) = σ2(n + 2) (see the number 1 079).
79 509 528
the ninth number n such that β(n)|β(n + 1) and β(n + 1)|β(n + 2): here 54|648
and 648|7950960 (see the number 225 504).
80 314 575
the smallest number n such that τ (n) τ (n + 1) . . . τ (n + 7): here
48 40 24 20 16 12 8 4 (see the number 45).
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