When sum of the factorials of the digits of integer equals to its reversed largest prime factor

 
 

The sum of the factorials of the digits of n is equal to the reversed largest prime factor of n
 
 

FACTORIALS 1

 

Find more examples

 
 
 
Paul found:

FACTORIALS 2

 

Paul made a list where the sum of all the prime factors of n is equal to the sum of the factorial of the digits of   n.

All   n \; \leq \; 10^6

 
FACTORIALS 3

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Advertisements

About benvitalis

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

4 Responses to When sum of the factorials of the digits of integer equals to its reversed largest prime factor

  1. paul says:

    Here are those <=1000000.
    Format is (n, Prime factors(n), last digit reversed, factorials of digits of n).

    311125 = {5,19,131}…..131 = {6,1,1,1,2,120}
    326244 = {2,3,31,877}…..778 = {6,2,720,2,24,24}
    326402 = {2,293,557}…..755 = {6,2,720,24,1,2}
    326433 = {3,233,467}…..764 = {6,2,720,24,6,6}
    331002 = {2,3,7,37,71}…..17 = {6,6,1,1,1,2}
    362401 = {13,61,457}…..754 = {6,720,2,24,1,1}
    421200 = {2,3,5,13}…..31 = {24,2,1,2,1,1}
    430000 = {2,5,43}…..34 = {24,6,1,1,1,1}
    441261 = {3,59,277}…..772 = {24,24,1,2,720,1}
    441440 = {2,5,31,89}…..98 = {24,24,1,24,24,1}
    444210 = {2,3,5,13,17,67}…..76 = {24,24,24,2,1,1}
    453550 = {2,5,47,193}…..391 = {24,120,6,120,120,1}
    511101 = {3,109,521}…..125 = {120,1,1,1,1,1}
    516261 = {3,37,4651}…..1564 = {120,1,720,2,720,1}
    521404 = {2,13,37,271}…..172 = {120,2,1,24,1,24}
    531302 = {2,421,631}…..136 = {120,6,1,6,1,2}
    603211 = {7,17,37,137}…..731 = {720,1,6,2,1,1}
    603240 = {2,3,5,11,457}…..754 = {720,1,6,2,24,1}
    630200 = {2,5,23,137}…..731 = {720,6,1,2,1,1}
    632212 = {2,7,67,337}…..733 = {720,6,2,2,1,2}
    651634 = {2,167,1951}…..1591 = {720,120,1,720,6,24}

    Paul.

  2. paul says:

    This is a list where the sum of all the prime factors of n is equal to the sum of the factorial of the digits of n. All n <=1000000

    1 = {1^1}…..1 = {1}
    2 = {2^1}…..2 = {2}
    1224 = {2^3,3^2,17^1}…..29 = {1,2,2,24}
    2401 = {7^4}…..28 = {2,24,1,1}
    4131 = {3^5,17^1}…..32 = {24,1,6,1}
    4212 = {2^2,3^4,13^1}…..29 = {24,2,1,2}
    12543 = {3^1,37^1,113^1}…..153 = {1,2,120,24,6}
    14345 = {5^1,19^1,151^1}…..175 = {1,24,6,24,120}
    14523 = {3^1,47^1,103^1}…..153 = {1,24,120,2,6}
    14655 = {3^1,5^1,977^1}…..985 = {1,24,720,120,120}
    15423 = {3^1,53^1,97^1}…..153 = {1,120,24,2,6}
    15462 = {2^1,3^2,859^1}…..867 = {1,120,24,720,2}
    30510 = {2^1,3^3,5^1,113^1}…..129 = {6,1,120,1,1}
    55430 = {2^1,5^1,23^1,241^1}…..271 = {120,120,24,6,1}
    66061 = {31^1,2131^1}…..2162 = {720,720,1,720,1}
    102226 = {2^1,79^1,647^1}…..728 = {1,1,2,2,2,720}
    103005 = {3^3,5^1,7^1,109^1}…..130 = {1,1,6,1,1,120}
    110215 = {5^1,7^1,47^1,67^1}…..126 = {1,1,1,2,1,120}
    126531 = {3^2,17^1,827^1}…..850 = {1,2,720,120,6,1}
    143543 = {23^1,79^2}…..181 = {1,24,6,120,24,6}
    145650 = {2^1,3^1,5^2,971^1}…..986 = {1,24,120,720,120,1}
    161230 = {2^1,5^1,23^1,701^1}…..731 = {1,720,1,2,6,1}
    163065 = {3^1,5^1,7^1,1553^1}…..1568 = {1,720,6,1,720,120}
    201115 = {5^1,19^1,29^1,73^1}…..126 = {2,1,1,1,1,120}
    202615 = {5^1,7^2,827^1}…..846 = {2,1,2,720,1,120}
    205543 = {13^1,97^1,163^1}…..273 = {2,1,120,120,24,6}
    210255 = {3^1,5^1,107^1,131^1}…..246 = {2,1,1,2,120,120}
    222462 = {2^1,3^2,17^1,727^1}…..752 = {2,2,2,24,720,2}
    223436 = {2^2,83^1,673^1}…..760 = {2,2,6,24,6,720}
    232165 = {5^1,59^1,787^1}…..851 = {2,6,2,1,720,120}
    266533 = {193^1,1381^1}…..1574 = {2,720,720,120,6,6}
    282401 = {7^1,40343^1}…..40350 = {2,40320,2,24,1,1}
    314432 = {2^6,17^3}…..63 = {6,1,24,24,6,2}
    350343 = {3^2,7^1,67^1,83^1}…..163 = {6,120,1,6,24,6}
    351106 = {2^1,7^1,31^1,809^1}…..849 = {6,120,1,1,1,720}
    353100 = {2^2,3^1,5^2,11^1,107^1}…..135 = {6,120,6,1,1,1}
    354320 = {2^4,5^1,43^1,103^1}…..159 = {6,120,24,6,2,1}
    354516 = {2^2,3^1,31^1,953^1}…..991 = {6,120,24,120,1,720}
    414000 = {2^4,3^2,5^3,23^1}…..52 = {24,1,24,1,1,1}
    416641 = {373^1,1117^1}…..1490 = {24,1,720,720,24,1}
    422415 = {3^4,5^1,7^1,149^1}…..173 = {24,2,2,24,1,120}
    434112 = {2^6,3^1,7^1,17^1,19^1}…..58 = {24,6,24,1,1,2}
    442000 = {2^4,5^3,13^1,17^1}…..53 = {24,24,2,1,1,1}
    451152 = {2^4,3^2,13^1,241^1}…..268 = {24,120,1,1,120,2}
    501125 = {5^3,19^1,211^1}…..245 = {120,1,1,1,2,120}
    501400 = {2^3,5^2,23^1,109^1}…..148 = {120,1,1,24,1,1}
    514155 = {3^1,5^1,151^1,227^1}…..386 = {120,1,24,1,120,120}
    514514 = {2^1,7^1,11^1,13^1,257^1}…..290 = {120,1,24,120,1,24}
    520542 = {2^1,3^2,11^2,239^1}…..269 = {120,2,1,120,24,2}
    533403 = {3^2,13^1,47^1,97^1}…..163 = {120,6,6,24,1,6}
    535031 = {7^2,61^1,179^1}…..254 = {120,6,120,1,6,1}
    621206 = {2^1,263^1,1181^1}…..1446 = {720,2,1,2,1,720}
    625212 = {2^2,3^3,7^1,827^1}…..847 = {720,2,120,2,1,2}

    Paul.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s