From ccc010ccb8a66278521500993d47208cbd7af66f Mon Sep 17 00:00:00 2001
From: Felix Martin <mail@felixm.de>
Date: Sat, 3 Oct 2026 13:36:16 -0400
Subject: [PATCH] Make solution for 401 faster

---
 python/e401.py | 21 +--------------------
 1 file changed, 1 insertion(+), 20 deletions(-)

diff --git a/python/e401.py b/python/e401.py
index d8de203..e6b0637 100644
--- a/python/e401.py
+++ b/python/e401.py
@@ -30,32 +30,13 @@ def sum2(a: int, b: int) -> int:
     return r
 
 
-def binsearch(a: int, d: int, n: int) -> int:
-    # Return the largest integer i in [a, n] for which n // i == d.
-
-    # Naive:
-    # b = a
-    # while n // (b + 1) == d:
-    #     b += 1
-    # return b
-
-    b = n
-    while n // b != d:
-        mid = (a + b) // 2
-        if b // mid != d:
-            b = mid
-        else:
-            a = mid
-    return b
-
-
 def sigma2caps(n: int) -> int:
     res = 0
     mod = 10**9
     a = 1
     while a <= n:
         d = n // a
-        b = binsearch(a, d, n)
+        b = n // d
         s2 = sum2(a, b) % mod
         res += (s2 * d) % mod
         res %= mod