```go
package main

import (
	"bufio"
	"fmt"
	"os"
)

func power(base, exp int64) int64 {
	res := int64(1)
	base %= 998244353
	for exp > 0 {
		if exp%2 == 1 {
			res = res * base % 998244353
		}
		base = base * base % 998244353
		exp /= 2
	}
	return res
}

func main() {
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanWords)

	buf := make([]byte, 1024*1024)
	scanner.Buffer(buf, 1024*1024*10)

	scanInt := func() int {
		scanner.Scan()
		res := 0
		for _, b := range scanner.Bytes() {
			res = res*10 + int(b-'0')
		}
		return res
	}

	scanInt64 := func() int64 {
		scanner.Scan()
		res := int64(0)
		for _, b := range scanner.Bytes() {
			res = res*10 + int64(b-'0')
		}
		return res
	}

	if !scanner.Scan() {
		return
	}
	m := 0
	for _, b := range scanner.Bytes() {
		m = m*10 + int(b-'0')
	}

	var cnt [100005]int64
	maxA := 0
	for i := 0; i < m; i++ {
		a := scanInt()
		f := scanInt64()
		cnt[a] += f
		if a > maxA {
			maxA = a
		}
	}

	mu := make([]int64, maxA+1)
	primes := make([]int, 0)
	isPrime := make([]bool, maxA+1)
	for i := 2; i <= maxA; i++ {
		isPrime[i] = true
	}

	mu[1] = 1
	for i := 2; i <= maxA; i++ {
		if isPrime[i] {
			primes = append(primes, i)
			mu[i] = -1
		}
		for _, p := range primes {
			if i*p > maxA {
				break
			}
			isPrime[i*p] = false
			if i%p == 0 {
				mu[i*p] = 0
				break
			} else {
				mu[i*p] = -mu[i]
			}
		}
	}

	ans := int64(0)
	inv8 := int64(873463809)
	P := int64(998244353)
	P1 := P - 1

	for d := 1; d <= maxA; d++ {
		if mu[d] == 0 {
			continue
		}
		Nd := int64(0)
		S1 := int64(0)
		S2 := int64(0)

		for i := d; i <= maxA; i += d {
			if cnt[i] > 0 {
				Nd += cnt[i]
				val := int64(i)
				cF := cnt[i] % P
				S1 = (S1 + val*cF) % P
				S2 = (S2 + (val*val%P)*cF) % P
			}
		}

		if Nd == 0 {
			continue
		}

		nModP := Nd % P
		nModP1 := Nd % P1

		pow2 := power(2, nModP1)
		term1 := (nModP - 2 + P) % P * S2 % P
		term2 := nModP * S1 % P * S1 % P
		Ed := pow2 * inv8 % P * ((term1 + term2) % P) % P

		if mu[d] == 1 {
			ans = (ans + Ed) % P
		} else if mu[d] == -1 {
			ans = (ans - Ed + P) % P
		}
	}

	fmt.Println(ans)
}
```