A336385 Number of k = x*y such that phi(k) = n*(phi(x) + phi(y)).
2, 5, 15, 14, 7, 25, 7, 36, 30, 26, 15, 68, 2, 21, 125, 78, 9, 94, 7, 90, 52, 33, 38, 208, 15, 11, 74, 69, 3, 227, 2, 166, 66, 33, 129, 276, 2, 25, 101, 228, 7, 115, 8, 76, 329, 47, 28, 482, 19, 65, 40, 50, 7, 248, 99, 234, 46, 34, 20, 572, 2, 5, 426, 356, 16
Offset: 1
Keywords
Examples
a(2) = 5 because k = 16, 24, 36, 40 and 60 satisfy the equation.
Links
- Zhang Sibao and Xi Xiaozhong, Positive integer solutions on phi(ab) = k*(phi(a) + phi(b))
Programs
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PARI
f(n) = floor(n*exp(Euler)*log(log(n^2))+2.5*n/log(log(n^2))); a(n) = {if(n==1, return(2)); my(t, v=List([])); for(x=1, f(2*n), if((t=eulerphi(x)) <= 2*n, for(y=1, f(t=n*t), if(eulerphi(x*y) == t+n*eulerphi(y), listput(v, x*y))))); #Set(v); }
Comments