Those Fascinating Numbers 287
3 653 786
the second number which is equal to the sum of the seventh powers of its digits
added to the product of its digits (see the number 455 226).
3 678 723
the smallest number n such that P (n + i)
3

n + i, for i = 0, 1, 2, 3: here
P (3678723) = P
(33
· 19 · 71 · 101) = 101 3

3678723 154, P (3678724) =
P
(22·72·1372)
= 137 3

3678724 154, P (3678725) = P
(52·37·41·97)
= 97
3

3678725 154 and P (3678726) = P (2 · 3 ·
832
· 89) = 89 3

3678726 154
(see the number 134 848).
3 741 154 (= 2 · 1 870 577)
the 1 000
000th
number having exactly two distinct prime factors (see the num-
ber 184).
3 768 373
the third number n such that Eσ(n) := σ(n + 1) σ(n) satisfies Eσ(n + 1) =
Eσ(n): here the common value of is 1 100 736, since σ(3768373) = 4560192,
σ(3768374) = 5660928 and σ(3768375) = 6761664 (see the number 693).
3 847 271
the smallest prime number p such that ω(p−1) = ω(p+1) = 6: here 3 847 270 =
2 · 5 · 7 · 17 · 53 · 61 and 3 847 272 = 23 · 3 · 11 · 13 · 19 · 59 (see the number 131).
3 885 569
the smallest prime number p such that Ω(p 1) = Ω(p + 1) = 10: here
3 885 568 =
29
· 7589 and 3 885 570 = 2 ·
36
· 5 · 13 · 41 (see the number 271).
3 995 648
the smallest number n such that n and n + 1 are both divisible by a ninth
power: 3 995 648 =
211
· 1951 and 3 995 649 =
39
· 7 · 29 (see the number 1 215).
4 037 913
the value of 1! + 2! + . . . + 10!.
4 046 849
the largest known prime number p such that P (p2 −1) 23 and P (p2 −1) = 23:
here
p2
1 =
215
·
32
·
52
· 13 · 17 · 19 ·
232
(see the number 4 801).
Previous Page Next Page