This property was first discovered in a phone book!

Number Theory Level 4

Let x x be a whole number that isn't prime and whose sum of digits in base 10 is equal to the sum of digits in its prime factorization. Find the sum of all such numbers less than 100.

The sum of digits in prime factorization of 26= 2*13 is 6 = 2+1+3.


The answer is 290.

Murlidhar Sharma by Murlidhar Sharma , 24, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Murlidhar Sharma
Jun 19, 2015

The numbers which satisfy the conditions are 4 , 22 , 27 , 58 , 85 , 94 4,22,27,58,85,94 (sequence A006753 in OEIS)

Such numbers are called Smith numbers. The first such number found was 4937775, here is the story about it : https://www.youtube.com/watch?v=mlqAvhjxAjo

0 Helpful 0 Interesting 0 Brilliant 0 Confused

I think the problem is not well redacted as it doesn't mention that you should sum up the digits of the prime factors. The problem says "... is equal to the sum of its prime factors ... " when the Smith numbers rule says "... is equal to the sum of the digits in its prime factorization." That's why I never came up with 22 as a number that meet the problem criteria.

Gustavo Cardenas - 5 years, 11 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...