## 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

Find more examples

Paul found:

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   $n \; \leq \; 10^6$

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.

• benvitalis says:

Thanks for doing this. I’ll post these results soon