Number theory problem(?)
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Is there an easier way to do this?
What is the sum of all counting numbers that have the property that the sum of their positive factors is 372.
A) 372
B) 601
C) 756
D) 906
E) Answer not given -
Could you post how you did it? Considering you said "easier way," you should already have a solution. How did you do it?
As a hint for a quicker way to do it:
I would first use the sum of factors formula:Let
$$n=p_1 ^{a_1}p_2^{a^2}p_3^{a_3} \ldots p_k^{a_k} $$(right now latex isn't displaying properly; sometimes it will have a line of math in plain text below the math in latex. Hope you still understand what I'm trying to show you)
The sum of the factors of
$$n $$is
$$(p_1^0+p_1^1+p_1^2+ \ldots + p_1^{a_1})(p_2^0+p_2^1+p_2^2+ \ldots + p^{a_2})\ldots (p_k^0+p_k^1+p_k^2 + \ldots + p_k^{a_k}) $$I would then prime factorize each of the answer choices and then apply the formula.
Hope this helps!
