Those Fascinating Numbers 185
10 693
the smallest 11-hyperperfect number (and the only one
108):
a number
n is said to be 11-hyperperfect if n = 1 + 11
d|n
1dn
d, which is equivalent to
11σ(n) = 12n + 10 (see the number 21).
10 790
the smallest solution of σ2(n) = σ2(n + 20); the sequence of numbers satisfying
this equation begins as follows: 10 790, 9 475 190, 13 622 390, 22 302 710, . . .
10 854
the smallest number n which allows the sum
m≤n
1
φ(m)
to exceed 18 (see the
number 177).
10 891
the smallest number n such that

m≤n
φ(m) is a multiple of 10 000 (here the
sum is equal to 36 060 000).
10 935
the sixth odd number n 1 such that γ(n)|σ(n) (see the number 135).
10 989
the third number which is not a palindrome and which divides the number
obtained by reversing its digits (see the number 1 089).
11 112
the second insolite number (see the number 111).
11 167
the smallest number n which allows the sum
m≤n
1
σ(m)
to exceed 7 (see the
number 129).
11 213
the exponent of the 23rd Mersenne prime 211 213 1 (Gillies, 1963).
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