Sum of Divisors

AtCoder

IDabc172_d

Time3000ms

Memory256MB

Difficulty—

For a positive integer $X$, let $f(X)$ be the number of positive divisors of $X$. Given a positive integer $N$, find $\sum_{K=1}^N K\times f(K)$. ## Constraints * $1 \leq N \leq 10^7$ ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

23

We have $f(1)=1$, $f(2)=2$, $f(3)=2$, and $f(4)=3$, so the answer is $1\times 1 + 2\times 2 + 3\times 2 + 4\times 3 =23$.

Input #2

Output #2

Input #3

10000000

Output #3

838627288460105

Watch out for overflows.

API Response (JSON)

{
  "problem": {
    "name": "Sum of Divisors",
    "description": {
      "content": "For a positive integer $X$, let $f(X)$ be the number of positive divisors of $X$. Given a positive integer $N$, find $\\sum_{K=1}^N K\\times f(K)$.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc172_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "For a positive integer $X$, let $f(X)$ be the number of positive divisors of $X$.\nGiven a positive integer $N$, find $\\sum_{K=1}^N K\\times f(K)$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^7$\n\n## Input\n\nI...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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