#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef tuple<int, int, int> tii;
typedef vector<int> vi;

#define pb push_back
#define eb emplace_back
#define all(s) (s).begin(), (s).end()
#define rep(i, a, b) for (int i = (a); i <= (b); ++i)
#define per(i, a, b) for (int i = (a); i >= (b); --i)

constexpr int N = 200007;

int npw[N];

string s;

int gcd(int a, int b) {return b ? gcd(b, a % b) : a;}

inline void work() {
    int a = 0, b = 0, c = 0;
    int ptr = 0;
    for (; s[ptr] != '^'; ++ptr) a = a * 10 + (s[ptr] - '0');
    ++ptr;
    for (; s[ptr] != '^'; ++ptr) b = b * 10 + (s[ptr] - '0');
    ++ptr;
    for (; ptr < s.size(); ++ptr) c = c * 10 + (s[ptr] - '0');
    auto decomp = [&](int x) {
        vector<pii> ret;
        for (int i = 2; i <= x; ++i)
            if (x % i == 0) {
                int num = 0;
                while (x % i == 0) {++num; x /= i;}
                ret.eb(i, num);
            }
        return ret;
    };
    auto da = decomp(a);
    int k = 0;
    for (auto [w, cnt] : da) k = gcd(k, cnt);
    map<int, int> num;
    auto dk = decomp(k);
    for (auto [w, cnt] : dk) num[w] = cnt;
    auto db = decomp(b);
    for (auto [w, cnt] : db) num[w] += cnt * c;
    ll ANS = 0;
    rep(cc, 2, N - 1) {
        ll ans = 1;
        for (auto [w, cnt] : num) ans = ans * ((cnt / cc) + 1);
        ANS += 1ll * (ans - 1) * npw[cc];
    }
    printf("%lld\n", ANS);
}

vector<pii> rts[N];

int main() {
    for (int i = 2; i < N; ++i) {
        ll nw = 1ll * i * i;
        for (int j = 2; nw < N; ++j) {
            rts[nw].eb(i, j);
            nw = nw * i;
        }
        npw[i] = 1;
        for (auto [rt, k] : rts[i]) npw[i] += npw[k];
    }
    cin.tie(0);
    ios::sync_with_stdio(false);
    while (cin >> s) work();
    return 0;
}