List questions from prime-factorization

Published on 03 Jul 2015 - 14:59

472

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What is the summatory function of the number of (not necessarily distinct) prime factors?

Published on 29 Mar 2026 - 3:37

6.5k

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Do prime numbers have prime factors?

Published on 06 Jul 2015 - 14:09

137

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Find all numbers that have 30 factors and have 30 as one of their factors.

Published on 06 Jul 2015 - 14:33

1.1k

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Calculation of product of all coprimes of number less than itself

Published on 06 Jul 2015 - 18:29

119

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Is there a way to estimate the number of positive integers less than or equal to $n$ that have a given prime $p$ as a least prime factor

Published on 06 Jul 2015 - 23:27

2k

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Is there a quicker way to generate integers which are hard to factor than multiplying two large primes?

Published on 27 Mar 2026 - 0:04

99

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Comparing $\pi(x)$ and $\pi^{(k)}(x)$

Published on 09 Jul 2015 - 21:41

69

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a new(?) operation using products of multiplicities

Published on 10 Jul 2015 - 1:03

305

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Number of unordered factorizations into $k$ distinct parts

Published on 12 Jul 2015 - 21:11

125

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$\text{lcm}(a,b)\cdot\text{lcm}(b,c)\cdot\text{lcm}(c,a)=a\cdot b\cdot c\cdot\text{gcd}(a,b,c)$,none a,b,c is integer multiple of any other of a,b,c.

Published on 14 Jul 2015 - 1:08

580

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GCD, LCM Relationship

Published on 30 Mar 2026 - 12:06

2.4k

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The number $2^{2^n} + 2^{2^{n - 1}} + 1$ can be expressed as the product of at least $n$ prime factors

Published on 18 Jul 2015 - 0:34

1k

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Prime factorization number theory

Published on 19 Jul 2015 - 22:28

714

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Largest Arithmetic Sum of Relatively Prime Numbers Under 30

Published on 20 Jul 2015 - 4:34

List Question

Inverse of prime counting function

What is the summatory function of the number of (not necessarily distinct) prime factors?

Do prime numbers have prime factors?

Find all numbers that have 30 factors and have 30 as one of their factors.

Calculation of product of all coprimes of number less than itself

Is there a way to estimate the number of positive integers less than or equal to $n$ that have a given prime $p$ as a least prime factor

Is there a quicker way to generate integers which are hard to factor than multiplying two large primes?

Comparing $\pi(x)$ and $\pi^{(k)}(x)$

a new(?) operation using products of multiplicities

Number of unordered factorizations into $k$ distinct parts

$\text{lcm}(a,b)\cdot\text{lcm}(b,c)\cdot\text{lcm}(c,a)=a\cdot b\cdot c\cdot\text{gcd}(a,b,c)$,none a,b,c is integer multiple of any other of a,b,c.

GCD, LCM Relationship

The number $2^{2^n} + 2^{2^{n - 1}} + 1$ can be expressed as the product of at least $n$ prime factors

Prime factorization number theory

Largest Arithmetic Sum of Relatively Prime Numbers Under 30

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