Those Fascinating Numbers 171
6 174 (= 2 · 32 · 73)
the value of the Kaprekar constant for the four digit numbers (see the number
495);
the fifth solution of φ(n) =
γ(n)2
(see the number 108).
6 185
the smallest number n such that the Liouville function λ0 takes successively,
starting with n, the values 1, −1, 1, −1, 1, −1, 1, −1, 1, −1, 1, −1; if nk stands for
the smallest number n such that λ0(n + i) =
(−1)i,
for i = 0, 1, 2, . . . , k 1,
then n2 = 4, n3 = 22, n4 = 49, n5 = n6 = n7 = 58, n8 = n9 = 342,
n10 = 1 230, n11 = n12 = 6 185, n13 = 4 9784, n14 = 79 800, n15 = n16 = n17 =
n18 = n19 = n20 = n21 = n22 = 99 826, n23 = 7 815 614, n24 = 11 435 684,
n25 = 19 370 102, n26 = 39 623 112, n27 = 46 025 769, n28 = n29 = 544 865 099
and n30 = 1 075 790 572.
6 200
the sixth number which is not perfect or multi-perfect but whose harmonic
mean is an integer (see the number 140).
6 247
the largest known number n such that
n!+2n
−1 is prime; the others are n = 1,
2, 3, 5, 7, 11, 167 and 2 609.
6 318
the first of the seven smallest consecutive numbers at which the Ω(n) function
takes distinct values, namely here the values 7, 2, 6, 4, 3, 1 and 5 (see the
number 726).
6 361
the smallest prime factor of the Mersenne number 253 1, whose complete
factorization is given by
253
1 = 6 361 · 69 431 · 20 394 401.
6 380
the
18th
number n such that n! + 1 is prime (see the number 116); note that
6 380! + 1 is a 21 507 digit number.
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