Số cô đơn

Science
Science
Vấn đề chưa được giải quyết trong Toán học : 10 có phải là một số cô đơn không?

Trong Lý thuyết số, số cô đơn đề cập đến một số nguyên dương mà không có bạn bè. Nếu hai số nguyên dương thỏa mãn σ(m)/m= σ (n)/n, trong đó σ(n) là hàm nhân tố, thì chúng được gọi là bạn bè, Hai số nguyên này là của nhau số tình bạn.

Ví dụ: (1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 40 + 80) / 80 = (1 + 2 + 4 + 5 + 8 + 10 + 20 + 25 + 40 + 50 + 100 + 200) / 200 = 93/40, vì vậy 80200 không phải là số cô đơn.

Tất cả n thỏa mãn (n, σ(n)) = 1 là các số đơn độc, vì vậy tất cả số nguyên tố power đều là số đơn độc. n, σ(n) không - coprime số đơn độc là 18, 45, 48,... (OEIS: A095739). Các số như 10, 14, 15, 20 không chứng minh được liệu đó có phải là một số cô đơn hay không.

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