Sublime number
An elevated number or sublime number is a natural number with the special property that the number of their division and its splitters sum perfect numbers are. So far only two raised numbers are known.
Well-known raised numbers
12
- and are perfect numbers.
6,086,555,670,238,378,989,670,371,734,243,169,622,657,830,773,351,885,970,528,324,860,512,791,691,264
6086555670238378989670371734243169622657830773351885970528324860512791691264
= 2 126 (2 61 - 1) (2 31 - 1) (2 19 - 1) (2 7 - 1) (2 5 - 1) (2 3 - 1).
This 76-digit raised number was discovered by Kevin Brown.
- The number of divisors is: (126 + 1) 2 6 = 8128.
- The sum of the divisors is: (2 126 + 1 -1) 2 61 + 31 + 19 + 7 + 5 + 3 = (2 127 -1) 2 126 .
- and are perfect numbers.
It is not known whether there are any other raised numbers or whether there could be an infinite number of or even odd raised numbers.
literature
- Clifford A. Pickover : Dr. Googol's wondrous world of numbers . Deutscher Taschenbuch-Verlag, Munich 2005, ISBN 3-423-34177-7 .
- Jean-Marie De Koninck: Those Fascinating Numbers. American Mathematical Society , Providence 2009, ISBN 978-0-8218-4807-4 , p. 4 ( online ) and p. 395 ( online ).