Number theory-Euler functions

One: Directly seeking Euler function

#include <cmath>#include<cstdio>#include<cstring>#include<iostream>#include<algorithm>using namespacestd;intMainvoid){    intN;  while(~SCANF ("%d",&N)) {intAns =N; intm = sqrt (n+0.5);  for(inti =2; I <= m; i++)        {            if(n==1)                 Break; if(n%i==0) {ans= ans/i* (I-1);  while(n%i==0) n= N/i; }        }        if(n!=1) ans= ans/n* (n1); printf ("%d\n", ans); }    return 0;}

Second: Play the table

#include <cmath>#include<cstdio>#include<cstring>#include<iostream>#include<algorithm>using namespacestd;Const intMAXN = -;intEULER[MAXN];voidInit () {euler[1]=1;  for(inti =2; I <= MAXN; i++) Euler[i]=i;  for(inti =2; I <= MAXN; i++)        if(euler[i]==i) for(intj = i; J <= Maxn; j+=i) euler[j]=euler[j]/i* (I-1);//Division first to prevent overflow of intermediate data}intMainvoid) {Init ();  for(inti =1; I <= MAXN; i++) {printf ("%d%d\n", I,euler[i]); }    return 0;}

Three: The linear sieve method of Euler's function

Principle:1: If P is prime, then φ (p) =p-1;

2: If i%p==0, then φ (i*p) =p*φ (i);

3: If i%p!=0, then φ (i*p) =φ (i) * (p-1)

#include <cmath>#include<cstdio>#include<cstring>#include<iostream>#include<algorithm>using namespacestd;Const intMAXN = -;intBOOK[MAXN];intPRIME[MAXN];intPHI[MAXN];intnum;voidInit () {memset (book,0,sizeof(book)); phi[1] =1; book[0] =1; book[1] =1;  for(inti =2; I <= MAXN; i++)     {        if(book[i]==0) {Prime[num++] =i; Phi[i]= i-1; }         for(intj =0; J < num; J + +)         {            intp =Prime[j]; if(I * p >MAXN) Break; Book[i* p] =1; Phi[i* p] = (i% p = =0? Phi[i] * p:phi[i] * (P-1)); if(i% P = =0)                  Break; }    }}intMainvoid) {Init ();  for(inti =1; i < MAXN; i++) printf ("%d%d\n", I,phi[i]); return 0;}

Number theory-Euler functions