Sum of gcd of Tuples (Easy)

AtCoder

IDabc162_c

Time2000ms

Memory256MB

Difficulty—

Find $\displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}$. Here $\gcd(a,b,c)$ denotes the greatest common divisor of $a$, $b$, and $c$. ## Constraints * $1 \leq K \leq 200$ * $K$ is an integer. ## Input Input is given from Standard Input in the following format: $K$ [samples]

Samples

Input #1

Output #1

9

$\gcd(1,1,1)+\gcd(1,1,2)+\gcd(1,2,1)+\gcd(1,2,2)$ $+\gcd(2,1,1)+\gcd(2,1,2)+\gcd(2,2,1)+\gcd(2,2,2)$ $=1+1+1+1+1+1+1+2=9$
Thus, the answer is $9$.

Input #2

Output #2

10813692

API Response (JSON)

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  "problem": {
    "name": "Sum of gcd of Tuples (Easy)",
    "description": {
      "content": "Find $\\displaystyle{\\sum_{a=1}^{K}\\sum_{b=1}^{K}\\sum_{c=1}^{K} \\gcd(a,b,c)}$. Here $\\gcd(a,b,c)$ denotes the greatest common divisor of $a$, $b$, and $c$.",
      "description_type": "Markdown"
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    "platform": "AtCoder",
    "limit": {
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      "memory_limit": 262144
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    "difficulty": "None",
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Find $\\displaystyle{\\sum_{a=1}^{K}\\sum_{b=1}^{K}\\sum_{c=1}^{K} \\gcd(a,b,c)}$.\nHere $\\gcd(a,b,c)$ denotes the greatest common divisor of $a$, $b$, and $c$.\n\n## Constraints\n\n*   $1 \\leq K \\leq 200$\n*   ...",
      "is_translate": false,
      "language": "English"
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