A new direction in number theory
Definition 1 (Papava). Natural number n colled rad-big number if rad(n)≥n/rad(n) or √n≤rad(n).
Definition 2 (Papava). Natural number n colled rad-little number if rad(n)<√n.
Definition 3 (Papava). A twin rad-little numbers is the twin rad-little pair (a,b) where a-b=2.
In first 1000 natural numbers there are only 56 rad-little numbers:
8,16,27,32,48,54,64,72,81,96,108,125,128,144,160,162,
192,200,216,224,243,250,256,288,320,324,343,375,384,
392,400,405,432,448,486,500,512,567, 576,625,640,648,675,686,704,729,768,784,800,832,864,
896,960,968,972,1000.
The rad-little numbers is infinity, because n^m is rad-little number when n>1 and m>2.
I find only one twin rad-little numbers (160; 162) in first 1000 natural numbers.
Conjecture 1 (Papava). The twin rad-little numbers are infinity.
Conjecture 2 (Papava). The twin rad-little numbers are finity.
A new direction in number theory Definition 1 (Papava). Natural number n colled rad-big number if rad(n)≥n/rad(n) or √n≤rad(n). Definition 2 (Papava). Natural number n colled rad-little number if rad(n)<√n. Definition 3 (Papava). A twin rad-little numbers is the twin rad-little pair (a,b) where a-b=2. In first 1000 natural numbers there are only 56 rad-little numbers: 8,16,27,32,48,54,64,72,81,96,108,125,128,144,160,162, 192,200,216,224,243,250,256,288,320,324,343,375,384, 392,400,405,432,448,486,500,512,567, 576,625,640,648,675,686,704,729,768,784,800,832,864, 896,960,968,972,1000. The rad-little numbers is infinity, because n^m is rad-little number when n>1 and m>2. I find only one twin rad-little numbers (160; 162) in first 1000 natural numbers. Conjecture 1 (Papava). The twin rad-little numbers are infinity. Conjecture 2 (Papava). The twin rad-little numbers are finity.
