A225536 - OEIS

%I #5 May 10 2013 14:07:39

%S 0,0,0,0,1,4,5,15,22,43,65,131,204,387,635,1136,2048,3727,6794,12296,

%T 22601,41746,76778,141923,263414,491925,917269,1718985,3225496,

%U 6067030,11435208,21593415,40858139

%N Numbers of triples {x, y, z} such that z >= y > 1 and prime(x) + prime(y) * prime(z) = 2^n.

%e 2^4 = 16 = 7 + 3*3, so a(4) = 1.

%e 2^5 = 32 = 7 + 5*5 = 11 + 3*7 = 17 + 3*5 = 23 + 3*3, so a(5) = 4.

%o (C)

%o #include <stdio.h>

%o #include <math.h>

%o #define TOP (1ULL<<32)

%o int main() {

%o   unsigned long long i, j, k, n, pp = 0, x, px, y, py, sr;

%o   unsigned int *primes = (unsigned int*)malloc(TOP/4);

%o   char *c = (char*)malloc(TOP/2);

%o   memset(c, 0, TOP/2);

%o   for (c[0] = i = 3; i < TOP; i+=2)

%o     if (c[i>>1]==0)

%o       for (primes[pp++]=i, j=i*i>>1; j<TOP/2; j+=i)  c[j]=1;

%o   for (n = 1; n <= TOP; n+=n) {

%o     for (k = x = 0; x < pp && (px = primes[x]) < n; ++x) {

%o       for (i=n-px, sr=sqrt(i), y=0; (py=primes[y])<=sr; ++y)

%o         if (i % py == 0) { if (c[i/py>>1] == 0) ++k; break; }

%o     }

%o     printf("%llu, ", k);

%o   }

%o }

%Y Cf. A000040, A006307, A225437.

%K nonn,more

%O 0,6

%A _Alex Ratushnyak_, May 10 2013