Those Fascinating Numbers 321
110 771 178
the sixth number n such that σ(φ(n)) = γ(n) (see the numbers 4 294 967 295
and 744).
111 111 111
the fourth insolite number (see the number 111).
113 315 400
the sixth number n such that φ(n) + σ(n) = 4n (see the number 23 760).
115 788 961 (=
412
· 68 881)
the smallest 40-hyperperfect number.
116 026 273
the smallest number n such that P (n+i) 4

n + i, i = 0, 1, 2: here 116 026 273 =
11 · 31 · 59 · 73 · 79, 116 026 274 = 2 · 7 · 132 · 19 · 29 · 89 and 116026275 =
3 · 52 · 172 · 53 · 101, while [
4

116026275] = 103; the sequence of numbers sa-
tisfying this property begins as follows: 116 026 273, 118 281 800, 196 512 875,
333 812 500, 390 881 412, . . . (see the number 134 848).
117 048 930
the smallest 7-composite number n such that n + 2 is also 7-composite (see the
number 1 428).
117 048 931
the smallest prime number p such that ω(p 1) = ω(p + 1) = 7: here
117 048 930 = 2 · 3 · 5 · 19 · 29 · 73 · 97 and 117 048 932 =
22
· 7 · 11 · 13 · 23 · 31 · 41
(see the number 131).
120 797 465
the smallest number n such that P (n) P (n + 1) . . . P (n + 10): here
24159493 20132911 17256781 2745397 1032457 416543 146777
54709 24953 19927 18097 (see the number 1 851).
122 121 216
the fifth insolite number (see the number 111); it is the smallest insolite number
containing the digit 6.
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