Rosetta Code

Talk:Abundant odd numbers: Difference between revisions

Page Discussion

Talk:Abundant odd numbers (view source)

Revision as of 17:05, 19 July 2021

1,401 bytes added ,  2 years ago
m
→‎On Number Theoretic Tasks: extended to 1e11 , to see, if it works
m (Undo revision 338251 by Horsth (talk))
m (→‎On Number Theoretic Tasks: extended to 1e11 , to see, if it works)
 
(One intermediate revision by the same user not shown)
Line 67:
==On Number Theoretic Tasks==
Perhaps we should have a tag "This solution is lame, please make it interesting and remove this tag". RC has too many tasks which are being solved by a loop which factorize a sequence of integers and then print something based on an if condition. Better would be if the author of these tasks indicated an interesting solution in the task description based on number theory. For this task I have added a reference which proves a number of properties of Odd Abundant numbers. 3 might be of interest to this task: there are no Odd abundant numbers with fewer than 3 prime factors; if a number is odd and abundant then so too are all odd multiple of that number; and Odd abundant numbers must satisfy the condition (p1/p1-1)*(p2/p2-1)..(pn/pn-1)>2. So p1=3,p2=5 then p3 must be less than 17 because (3/2)*(5/4)*(13/12)=2.03125 and (3/2)*(5/4)*(17/16)=1.9921875. Errors in early implementations uncovered the smallest Odd abundant number not divisible by 5. Let me consider p1=3, p2=7 and p3=11. (3/2)*(7/6)*(11/10)=1.9250000000000003 so there are no Odd abundant numbers not divisible by 5 with 3 prime factors. So p1=3, p2=7, p3=11, p4=13 -> (3/2)*(7/6)*(11/10)*(13/12)=2.0854166666666667 so this is a good place to start looking. So what is the smallest Odd abundant number not divisible by 3?--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 21:29, 19 May 2019 (UTC)
:So what is the smallest Odd abundant number not divisible by 3:
-<pre>// ### without 5
<pre>From zumkeller numbers, check every 20/10 th: 5/25/35/55 ...
1: 81081= 3^4*7*11*13
20: 5391411025 :384 : 153153= 35^2*7*11*13*17*19*23*29 _chk_5391411025_SoD_10799308800// sum of divisors
31:26957055125 :512 : 171171= 35^23*7*11*13*17*19*23*29 _chk_26957055125_SoD_54344908800
2:28816162375 :512 : 5^3*7*11*13*17*19*23*31 _chk_28816162375_SoD_57967902720
4: 189189= 3^3*7^2*11*13
53:33426748355 :512 : 207207= 3^25*7*11*13*17*19*23*29*31 _chk_33426748355_SoD_66886041600
64:34393484125 :512 : 223839= 35^23*7*11*13*17*19*23*37 _chk_34393484125_SoD_68836884480
5:37739877175 :576 : 5^2*7^2*11*13*17*19*23*29_chk_37739877175_SoD_76945075200
7: 243243= 3^5*7*11*13
86:40342627325 :576 : 261261= 35^2*7^2*11*13*2917*19*23*31_chk_40342627325_SoD_82074746880
97:48150877775 :576 : 279279= 35^2*7^2*11*13*3117*19*23*37_chk_48150877775_SoD_97463761920
8:50866790975 :576 : 5^2*7^2*11*13*17*19*29*31_chk_50866790975_SoD_102593433600
10: 297297= 3^3*7*11^2*13
9:53356378075 :576 : 5^2*7^2*11*13*17*19*23*41_chk_53356378075_SoD_107723105280
 
10:55959128225 :576 : 5^2*7^2*11*13*17*19*23*43_chk_55959128225_SoD_112852776960
1000: 31612581= 3^2*7*11^3*13*29
11:59305521275 :576 : 5^2*7*11^2*13*17*19*23*29_chk_59305521275_SoD_119692339200
Min Delta 1386
12:60711976325 :576 : 5^2*7^2*11*13*17*19*29*37_chk_60711976325_SoD_121829702400
 
13:61164628525 :576 : 5^2*7^2*11*13*17*19*23*47_chk_61164628525_SoD_123112120320
The first abundant odd number above one billion is: 1000026027= 3^3*7*11*13*163*22
14:63395557225 :576 : 5^2*7*11^2*13*17*19*23*31_chk_63395557225_SoD_127671828480
// ### without 5,7
15:64899009175 1:576 : 28683369= 35^32*7^2*11*13*17*19*2331*37_chk_64899009175_SoD_129951682560
16:67275433225 2:576 : 36165987= 35^32*7^2*11*13*17*19*29*41_chk_67275433225_SoD_134653881600
17:68972878975 3:576 : 38660193= 35^32*7^2*11*13*17*19*3123*53_chk_68972878975_SoD_138501135360
18:70088343325 4:576 : 86050107= 35^42*7*11*13^2*17*19*23*29_chk_70088343325_SoD_141162393600
19:74922022175 5:576 : 108497961= 35^42*7*11*13^2*17*19*2923*31_chk_74922022175_SoD_150573219840
20:75665665075 6:576 : 115980579= 35^42*7*11^2*13*17*19*3123*37_chk_75665665075_SoD_151610296320
21:76781129425 7:576 : 131339637= 35^42*7^2*11*13*17*19*23*2959_chk_76781129425_SoD_153890150400
22:79383879575 8:576 : 138428433= 35^42*7^2*11*13*17*19*3723*61_chk_79383879575_SoD_159019822080
23:87192130025 9:576 : 140397543= 35^42*7^2*11*13*17*19*23*3167_chk_87192130025_SoD_174408837120
1024:91653987425 :576 153393669=: 35^42*7*11*13*17^2*19*4123*29_chk_91653987425_SoD_184188211200
25:97974952075 :576 : 5^2*7*11*13*17^2*19*23*31_chk_97974952075_SoD_196467425280
Min Delta 1969110
real 76m32,432s
 
</pre> -[[User:Horsth|Horsth]] 15:20, 19 July 2021 (UTC)
The first abundant odd number above one billion is: 1043825211= 3^6*11*13*17*19*31</pre>
Anonymous user
Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/290499...290501"