C++ :

#pragma GCC optimize ("O2")
#include <cmath>
#include <vector>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;

typedef long long ll;
const int N=50666;
#define mod 1000000007
typedef pair<int,ll> pi;
#define mp(a,b) make_pair(a,b)

int A,B,C,du[N];
ll ans,sa[N],sb[N],sc[N];
int top,list[N],mu[N];
bool vis[N];
vector<pi>vec[N];

void prepare(int n=50000) {
	mu[1]=1;
	for (int i=2;i<=n;i++) {
		if (!vis[i]) {list[++top]=i;mu[i]=-1;}
		for (int j=1;j<=top&&i*list[j]<=n;j++){
			vis[i*list[j]]=1;
			if (i%list[j]) mu[i*list[j]]=-mu[i];
			else {mu[i*list[j]]=0;break;}
		}
	}
}

void calc1() {
	for (int i=1;i<=C;i++) ans+=(ll)sa[i]*sb[i]*sc[i]*mu[i]*mu[i]*mu[i];
}

void calc2() {
	for (int gcd=1;gcd<=C;gcd++)
	for (int lcm=gcd;lcm<=C;lcm+=gcd) if (mu[gcd]&&mu[lcm]){
		for (int i=1;i*i<=lcm/gcd;i++) if ((lcm/gcd)%i==0){
			int x=i*gcd,y=lcm/i; if (x>=y) continue;
			du[x]++,du[y]++;
			ans+=(ll)mu[x]*mu[x]*mu[y]*sa[x]*sb[lcm]*sc[lcm];
			ans+=(ll)mu[x]*mu[y]*mu[x]*sa[lcm]*sb[x]*sc[lcm];
			ans+=(ll)mu[y]*mu[x]*mu[x]*sa[lcm]*sb[lcm]*sc[x];
			ans+=(ll)mu[x]*mu[y]*mu[y]*sa[lcm]*sb[lcm]*sc[y];
			ans+=(ll)mu[y]*mu[x]*mu[y]*sa[lcm]*sb[y]*sc[lcm];
			ans+=(ll)mu[y]*mu[y]*mu[x]*sa[y]*sb[lcm]*sc[lcm];
		}
	}
}

void calc3() {
	for (int gcd=1;gcd<=C;gcd++)
	for (int lcm=gcd;lcm<=C;lcm+=gcd)if (mu[gcd]*mu[lcm]){
		for (int i=1;i*i<=lcm/gcd;i++) if ((lcm/gcd)%i==0){
			int x=i*gcd,y=lcm/i; if (x>=y) continue;
			if (du[x]>du[y]) swap(x,y);
			vec[x].push_back(mp(y,lcm));
		}
	}
	for (int i=1;i<=C;i++) sort(vec[i].begin(),vec[i].end());
	for (int i=1;i<=C;i++)
	for (int j=0;j<(int)vec[i].size();j++) {
		int k=vec[i][j].first; int p1,p2; p1=p2=0;
		while (p1<vec[i].size()&&p2<vec[k].size()) {
			if (vec[i][p1].first==vec[k][p2].first){
				int x=vec[i][p1].first;
				ans+=(ll)mu[i]*mu[k]*mu[x]*sa[vec[i][j].second]*sb[vec[i][p1].second]*sc[vec[k][p2].second];
				ans+=(ll)mu[i]*mu[x]*mu[k]*sa[vec[i][p1].second]*sb[vec[i][j].second]*sc[vec[k][p2].second];
				ans+=(ll)mu[k]*mu[i]*mu[x]*sa[vec[i][j].second]*sb[vec[k][p2].second]*sc[vec[i][p1].second];
				ans+=(ll)mu[k]*mu[x]*mu[i]*sa[vec[k][p2].second]*sb[vec[i][j].second]*sc[vec[i][p1].second];
				ans+=(ll)mu[x]*mu[i]*mu[k]*sa[vec[i][p1].second]*sb[vec[k][p2].second]*sc[vec[i][j].second];
				ans+=(ll)mu[x]*mu[k]*mu[i]*sa[vec[k][p2].second]*sb[vec[i][p1].second]*sc[vec[i][j].second];
				p1++,p2++;
			}else if (vec[i][p1].first<vec[k][p2].first) p1++;
			else if (vec[i][p1].first>vec[k][p2].first) p2++;
		}
	}
}

int main(){
	prepare();
	scanf("%d%d%d",&A,&B,&C);
	if (A>B) swap(A,B);
	if (A>C) swap(A,C);
	if (B>C) swap(B,C);
	for (int i=1;i<=C;i++) for (int j=i;j<=A;j+=i) sa[i]++;
	for (int i=1;i<=C;i++) for (int j=i;j<=B;j+=i) sb[i]++;
	for (int i=1;i<=C;i++) for (int j=i;j<=C;j+=i) sc[i]++;
	ans=0;
//	puts("fcuk");
	calc1();
	calc2();
//	puts("fcujk");
	calc3();
//	puts("fcuk");
	printf("%lld\n",(ans%mod+mod)%mod);
//	while (1);
	return 0;
}