20180402, 23:56  #1 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
The natural progression of (even perfect numbers)*3
Is there an OEIS entry for this sequence (starting with f(0)=3)?
Or, as a corollary, the secondary sequence g(n) where g(n) is the first index of f(n) which is divisible by the nth Mersenne prime? Such that we know at least the first 873 terms of f(n); meanwhile g(1) = 0, g(2) = 2, g(3) = 29, with g(5) unknown as evidenced by this thread? (Of course Mp  f(n) does not guarantee that the nth term loses the Mp driver, but it does mean that the sequence diverges from the f sequence.) 
20180403, 00:12  #2  
Nov 2008
912_{16} Posts 
Quote:
Quote:
Last fiddled with by 10metreh on 20180403 at 00:12 

20180403, 00:26  #3  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
Quote:
Quote:


20180403, 12:25  #4 
Nov 2008
100100010010_{2} Posts 

20180509, 12:37  #5  
"Garambois JeanLuc"
Oct 2011
France
1010111111_{2} Posts 
Quote:
Starting with f(0)=2, we have : 2, 4, 10, 26, 58, 122, 250, 686 ... There is no OEIS entry for this sequence. Just for fun, I calculated the first 348 terms of this sequence. Curiously, we do not find the prime number 3 in the decomposition into prime numbers of these terms. You can see here : http://www.aliquotes.com/parfait_2_z.txt 

20180515, 12:43  #6 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
1110000110101_{2} Posts 

20180515, 15:59  #7 
Romulan Interpreter
"name field"
Jun 2011
Thailand
9,859 Posts 
As we start with a number n which is either 1 or 2 (mod 3) and 0 (mod 2), it means this is either 2 or 4 (mod 6). If its sigma is 0 (mod 3), then we have the next term t=2*sigman is either t=2*01=2 (mod 3) or t=2*02=1 (mod 3). So the only combinations that would result in 0 (mod 3) are either (A) n=4 (mod 6) and sigma(n)=2 (mod 3) or (B) n=2 (mod 6) and sigma(n)=1 (mod 3). We can expand some formulae for sigma and see if we can get this, considering that if n=1 (mod 3) than its prime factors which are 2 (mod 3) can be grouped twobytwo in those products for sigma, etc.

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Prime Numbers as a Function of a Geometric Progression  danupp  And now for something completely different  2  20171104 17:55 
Odd Perfect Numbers  davar55  Miscellaneous Math  16  20110129 01:53 
Proof of Perfect Numbers  Vijay  Miscellaneous Math  10  20050528 18:11 
Perfect Numbers  MajUSAFRet  Math  3  20031213 03:55 
Odd Perfect Numbers  ZetaFlux  Math  1  20030528 19:41 