35 lines
1.2 KiB
Text
35 lines
1.2 KiB
Text
A '''Duffinian number''' is a composite number '''k''' that is relatively prime to its sigma sum '''σ'''.
|
||
|
||
''The sigma sum of '''k''' is the sum of the divisors of '''k'''.''
|
||
|
||
|
||
;E.G.
|
||
|
||
'''161''' is a '''Duffinian number'''.
|
||
* It is composite. (7 × 23)
|
||
* The sigma sum '''192''' (1 + 7 + 23 + 161) is relatively prime to '''161'''.
|
||
|
||
|
||
Duffinian numbers are very common.
|
||
|
||
It is not uncommon for two consecutive integers to be Duffinian (a Duffinian twin) (8, 9), (35, 36), (49, 50), etc.
|
||
|
||
Less common are Duffinian triplets; three consecutive Duffinian numbers. (63, 64, 65), (323, 324, 325), etc.
|
||
|
||
Much, much less common are Duffinian quadruplets and quintuplets. The first Duffinian quintuplet is (202605639573839041, 202605639573839042, 202605639573839043, 202605639573839044, 202605639573839045).
|
||
|
||
It is not possible to have six consecutive Duffinian numbers
|
||
|
||
|
||
;Task
|
||
* Find and show the first 50 Duffinian numbers.
|
||
* Find and show at least the first 15 Duffinian triplets.
|
||
|
||
|
||
;See also
|
||
;* [https://www.numbersaplenty.com/set/Duffinian_number Numbers Aplenty - Duffinian numbers]
|
||
;* [[oeis:A003624|OEIS:A003624 - Duffinian numbers: composite numbers k relatively prime to sigma(k)]]
|
||
|
||
|
||
|
||
|