# Tagged Questions

70 views

### How to find sum of factors of $2^{2012}$?

This question really is confusing me and I was wondering if there was a simple way this could be achieved. I've come up with this so far... $\sum_{n=0}^{2012} 2^n$ PS. Please forgive me for my ...
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### Decomposability of a function into two

This is question on the existence of a decomposability of a function $f(v)$ into multiplicative factors $\lambda(v)$ and $g(v)$. The question is non-trivial since the functions $\lambda(v)$ and $g(v)$ ...
154 views

### Solve $a^3 + b^3 + c^3 = 6abc$

Find solutions for $a^3 + b^3 + c^3 = 6abc$ in $\mathbb{N}$, such that $gcd(a,b,c) = 1$, except for $(1,2,3)$ and its permutations. Using trial and error I found out that if $a,b,c$ are solution ...
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### Sum of number of factors of first N numbers [duplicate]

Given a number N ( Value can be large like N < 10^9 ) How can we calculate sum of the number of factors of first N numbers?? Example : For n = 3 Answer: = #f(1) + #f(2) + #f(3) --- { #f(n) ...
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### Does this sequence have this interesting property relating to the prime factorization of the index?

Define a sequence as $a_0 = 0$ and $a_n$ equals the number of divisors of $n$ (including 1 and $n$) that are greater than $a_{n-1}$. This is sequence A152188 in OEIS, by the way. (For example, the ...
### Help with $1 + a + a(a-1) + a(a-1) (a-2) +\cdots+a(a-1)\cdots(a-(n-1))$
I want to rewrite the series $$1 + a + a(a-1) + a(a-1) (a-2) +\cdots+a(a-1)\cdots(a-(n-1))$$ as $(a^n-1)Y$ or $(a^{n-1}-1)Y$ Short-form: $$\{1+\sum_{i=1}^{n} \prod_{j=0}^{i-1}(a-j)\}$$ as $(a^n-1)Y$ ...