Num3er 2016 – sum of all the divisors

 
 

\sigma_1 \, (N)   is the sum of all the divisors of   N
 

\sigma_1 \, (672) \; = \; 2016 \; = \; 3 \; \times \; 672

 

Find other values for   N   for which   \sigma_1 \, (N) \; = \; 3 \, N

 
 

 

Numbers of the form   2^n \; \times \; 3 \; \times \; p   may satisfy the condition
 

  n = 3   —>   120 \; = \; 2^3 \times 3 \times 5
     \sigma_1 \, (120) \; = \; 360  \; = \; 3 \; \times \; 672
 

  n = 4   —>   ….
 

  n = 5   —>   672 \; = \; 2^5 \times 3 \times 7
     \sigma_1 \, (672) \; = \; 2016 \; = \; 3 \; \times \; 672
 

  n = 6   —>   ….
 

  n = 7   —>   ….
 

  n = 8   —>   459818240 \; = \; 2^8 \times 5 \times 7 \times 19 \times 37 \times 73
     \sigma_1 \, (459818240) \; = \; 1379454720 \; = \; 3 \; \times \; 459818240
 

  n = 9   —>   523776 \; = \; 2^9 \times 3 \times 11 \times 31
     \sigma_1 \, (523776) \; = \; 1571328 \; = \; 3 \; \times \; 523776
 

n = 10   —>   ….
 

n = 11   —>   ….
 

n = 12   —>   ….
 

n = 13   —>   1476304896 \; = \; 2^{13} \times 3 \times 11 \times 43 \times 127
     \sigma_1 \, (1476304896) \; = \;  4428914688 \; = \; 3 \; \times \; 1476304896
 

n = 14   —>   51001180160 \; = \; 2^{14} \times 5 \times 7 \times 19 \times 31 \times 151
     \sigma_1 \, (51001180160) \; = \; 153003540480 \; = \; 3 \; \times \; 51001180160
 

n = 15   —>   ….

…………
…………
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged , . Bookmark the permalink.

2 Responses to Num3er 2016 – sum of all the divisors

  1. paul says:

    Here are 2 more

    d(120) = 360 = 3 x 120
    d(523776) = 1571328 = 3 x 523776

    Paul

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