local mce, mfl, msq, mmi, mma, mab = math.ceil, math.floor, math.sqrt, math.min, math.max, math.abs local mod = 1000000007 local function bmul(x, y) local x1, y1 = mfl(x / 31623), mfl(y / 31623) local x0, y0 = x - x1 * 31623, y - y1 * 31623 return (x1 * y1 * 14122 + (x1 * y0 + x0 * y1) * 31623 + x0 * y0) % mod end local function badd(x, y) return (x + y) % mod end local function getprimes(x) local primes = {} local allnums = {} for i = 1, x do allnums[i] = true end for i = 2, x do if allnums[i] then table.insert(primes, i) local lim = mfl(x / i) for j = 2, lim do allnums[j * i] = false end end end return primes end local function getdivisorparts(x, primes) local prime_num = #primes local tmp = {} local lim = mce(msq(x)) local primepos = 1 local dv = primes[primepos] while primepos <= prime_num and dv <= lim do if x % dv == 0 then local t = {} t.p = dv t.cnt = 1 x = mfl(x / dv) while x % dv == 0 do x = mfl(x / dv) t.cnt = t.cnt + 1 end table.insert(tmp, t) lim = mce(msq(x)) end if primepos == prime_num then break end primepos = primepos + 1 dv = primes[primepos] end if x ~= 1 then local t = {} t.p, t.cnt = x, 1 table.insert(tmp, t) end return tmp end local function getdivisorCore(divisorparts) local t = {} local pat = 1 local len = #divisorparts local allpat = 1 for i = 1, len do allpat = allpat * (1 + divisorparts[i].cnt) end for t_i_pat = 0, allpat - 1 do local div = allpat local i_pat = t_i_pat local ret = 1 for i = 1, len do div = mfl(div / (divisorparts[i].cnt + 1)) local mul = mfl(i_pat / div) i_pat = i_pat % div for j = 1, mul do ret = ret * divisorparts[i].p end end table.insert(t, ret) end -- table.sort(t) return t end local function getdivisor(x, primes) local dvp = getdivisorparts(x, primes) return getdivisorCore(dvp) end local n = io.read("*n") local primes = getprimes(mce(msq(n))) local t = {} t[1] = 1 for i = 2, n do local dvs = getdivisor(i, primes) local c = 1 for j = 1, #dvs - 1 do local dv = dvs[j] local rem = mfl(i / dv) - 1 c = badd(c, t[rem]) end t[i] = c end print(t[n])