Data commit

Task/Amicable-pairs/C/amicable-pairs.c

@@ -0,0 +1,56 @@
+#include <stdio.h>
+#include <stdlib.h>
+
+typedef unsigned int uint;
+
+int main(int argc, char **argv)
+{
+  uint top = atoi(argv[1]);
+  uint *divsum = malloc((top + 1) * sizeof(*divsum));
+  uint pows[32] = {1, 0};
+
+  for (uint i = 0; i <= top; i++) divsum[i] = 1;
+
+  // sieve
+  // only sieve within lower half , the modification starts at 2*p
+  for (uint p = 2; p+p <= top; p++) {
+    if (divsum[p] > 1) {
+      divsum[p] -= p;// subtract number itself from divisor sum ('proper')
+      continue;}     // p not prime
+
+    uint x; // highest power of p we need
+    //checking x <= top/y instead of x*y <= top to avoid overflow
+    for (x = 1; pows[x - 1] <= top/p; x++)
+      pows[x] = p*pows[x - 1];
+
+    //counter where n is not a*p with a = ?*p, useful for most p.
+    //think of p>31 seldom divisions or p>sqrt(top) than no division is needed
+    //n = 2*p, so the prime itself is left unchanged => k=p-1
+    uint k= p-1;
+    for (uint n = p+p; n <= top; n += p) {
+      uint s=1+pows[1];
+      k--;
+      // search the right power only if needed
+      if ( k==0) {
+        for (uint i = 2; i < x && !(n%pows[i]); s += pows[i++]);
+        k = p; }
+      divsum[n] *= s;
+    }
+  }
+
+  //now correct the upper half
+  for (uint p = (top >> 1)+1; p <= top; p++) {
+    if (divsum[p] > 1){
+      divsum[p] -= p;}
+  }
+
+  uint cnt = 0;
+  for (uint a = 1; a <= top; a++) {
+    uint b = divsum[a];
+    if (b > a && b <= top && divsum[b] == a){
+      printf("%u %u\n", a, b);
+      cnt++;}
+  }
+  printf("\nTop %u count : %u\n",top,cnt);
+  return 0;
+}