local mce, mfl, msq, mmi, mma, mab = math.ceil, math.floor, math.sqrt, math.min, math.max, math.abs local bls, brs = bit.lshift, bit.rshift local bor, band = bit.bor, bit.band local BITBOX = {} BITBOX.initialize = function(self, lim) self.lim = lim self.sz = 30 self.way = true self.bcnt = mce(lim / self.sz) self.b1 = {} for i = 1, self.bcnt do self.b1[i] = 0 end self.curmax = 0 end BITBOX.set = function(self, x) local group = mce(x / self.sz) local idx = x - (group - 1) * self.sz self.b1[group] = bor(self.b1[group], bls(1, idx - 1)) end BITBOX.query = function(self, x) local group = mce(x / self.sz) local idx = x - (group - 1) * self.sz return band(self.b1[group], bls(1, idx - 1)) ~= 0 end BITBOX.new = function(n) local obj = {} setmetatable(obj, {__index = BITBOX}) obj:initialize(n) return obj end local bbprime = BITBOX.new(50000000) local bbsq = BITBOX.new(50000000) local function comp(a, b) return a < b end local function lower_bound(ary, x) local num = #ary if num == 0 then return 1 end if not comp(ary[1], x) then return 1 end if comp(ary[num], x) then return num + 1 end local min, max = 1, num while 1 < max - min do local mid = mfl((min + max) / 2) if comp(ary[mid], x) then min = mid else max = mid end end return max end local function getprimes(x) local primes = {} local withsq = {1} for i = 2, x do if bbsq:query(i) then table.insert(withsq, i) end if not bbprime:query(i) then table.insert(primes, i) local lim = mfl(x / i) for j = 2, lim do bbprime:set(j * i) end if 4 < i then lim = mfl(x / (i * i)) for j = 1, lim do if 0 < j % 4 and 0 < j % 9 then bbsq:set(j * i * i) end end end end end return primes, withsq end local n = io.read("*n") local primes, withsq = getprimes(n) -- print(table.concat(withsq, " ")) -- print(#primes, #withsq) -- print(os.clock()) local t = {} local baselim = 1 while (baselim + 1) * (baselim + 1) <= n do baselim = baselim + 1 end local ans = baselim * baselim for base = 1, baselim do local cnt = mfl(n / (base * base)) local lb = lower_bound(withsq, cnt + 1) cnt = cnt - mfl(cnt / 4) - mfl(cnt / 9) + mfl(cnt / 36) - (lb - 1) ans = ans + cnt * (2 * base - 1) end print(ans) -- print(os.clock())