Those Fascinating Numbers 309
34 385 818
the seventh even number n such that σI (n) = σI (n+2) (see the number 54 178).
35 020 303
the ninth composite number n such that σ(n + 6) = σ(n) + 6 (see the number
104).
35 080 502
the eighth even number n such that σI (n) = σI (n +2) (see the number 54 178).
35 357 670
the
16th
Catalan number (see the number 14).
35 515 634
the smallest number n such that ω(n) + ω(n + 1) + ω(n + 2) = 17: here
35 515 634 = 2 · 7 · 11 · 23 · 37 · 271, 35 515 635 = 3 · 5 · 17 · 41 · 43 · 79 and
35 515 636 = 22 · 13 · 19 · 103 · 349 (see the number 2 210).
36 171 409
the largest known prime number p such that P
(p2
−1) 29 and P
(p2
−1) = 29:
here
p2
1 =
25
· 3 · 5 ·
73
· 11 ·
133
· 17 · 23 ·
292
(see the number 4 801).
36 197 180 (=
25
·
35
· 5 ·
72
· 19)
the second solution of
σ(n)
n
=
13
3
(see the number 18 506 880).
36 315 135
the smallest number n such that n and n + 1 are both divisible by an eleventh
power: here 36 315 135 =
311
· 5 · 41 and 36 315 136 =
213
· 11 · 13 · 31 (see the
number 1 215).
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