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> 1 , , - , ( , , 1, , , ). , n = p1*p2*...*pk, . , 24=2*2*2*3. , . , .

. , 2 520 2520 = 23 2 5 7. : n (1), : (2)

, , d (2) . d , a=cd, , , d , . , : ) (n) - n; 2) (n) - n. n (1). .

1. n
. (2). 1 0,1,2,...1, 1+1 ( 1, 1, 1^2,...1^1) , 2 0,1,2,...2, 2+1 ( 1, 2, 2^2,...2^2) .. k 0,1,2,...k, k+1 ( 1, k, k^2,...k^k). 1+1 , 1, 2+1 2 . ., , n . 2 520 = 23 2 5 7. (3+1)(2+1)(1+1)(1+1) = 48 .

2. n (1). n
.
, :
(4)
(4)

n, . (4') n, . . (n) . , (n) (4). , 1+m+ m2+...+ mm 1 m. (4) :
(5)
. 90. 90=2 2 5. (90)=[(22-1)/(2-1)] [3-1)/(3-1)] [(52-1)/(5-1)]=234 (4) ., , 90, ( ): (1+2)(1+3+2)(1+5)=(1+1*3+1*2+1*2+2*3+2*2)(1+5) = 1+3+2+2+2*3+2*2+ 5+3*5+2*5+2*5+2*3*5+2*2*5 = 1+3+9+2+6+18+5+15+45+10+30+90 - 90.

. , , , 6, 28. . n , n= 1122 ( , 1 < 2). 6, (3) (1+1)(2+1)=6. , 2 (1,21), 6 6=23 , 1)

(1+ 1+ 12)(1+2)=28, 1+ 1+ 12 > 3, 1+2 >3. 1+ 1+ 12=4, 1+2=7 ( ) 1+ 1+ 12=7, 1+2=4, 1=2, 2=3

n=22 3=12
28, (1+1)(1+ 2+ 22)=28. 28 : 28=1*28=2*14=4*7 ( ) , 1 < 1 < 2, 2 > 2, , 1+1 >2, 1+ 2+ 22 >7. 28 2)

. 1. , 2 , 8 , 60. 2. , 3 4 21 . 3. , 18 . 4. , 5, 18 . 5. . 15 . ? 6. . 81 . ? 7. m = 2x3y5z, , 30 , 35 42 , .