A308342 Number of ways to write 2*n as phi(x^2) + phi(y^2) + phi(z^2), where x,y,z are positive integers with x <= y <= z, and phi(.) is Euler's totient function (A000010).
0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 1, 2, 3, 4, 4, 3, 4, 5, 4, 6, 5, 5, 5, 5, 5, 5, 4, 5, 4, 4, 2, 5, 5, 3, 6, 6, 3, 7, 6, 6, 6, 5, 6, 6, 4, 5, 5, 5, 5, 6, 4, 5, 8, 7, 5, 9, 6, 7, 8, 8, 7, 6, 6, 8, 5, 7, 7, 6, 5, 6, 8, 8, 8, 10, 6, 10, 13, 10, 10, 9, 6, 11, 9, 7, 3, 9, 6, 6, 9, 7, 5, 12
Offset: 1
Keywords
Examples
a(2) = 1 with 2*2 = phi(1^2) + phi(1^2) + phi(2^2). a(3) = 1 with 2*3 = phi(2^2) + phi(2^2) + phi(2^2). a(4) = 1 with 2*4 = phi(1^2) + phi(1^2) + phi(3^2). a(6) = 1 with 2*6 = phi(2^2) + phi(2^2) + phi(4^2). a(19) = 1 with 2*19 = phi(3^2) + phi(5^2) + phi(6^2).
Links
- Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
- Zhi-Wei Sun, Does phi(x^2) + phi(y^2) + phi(z^2) represent all even numbers greater than two?, Question 332067 on MathOverflow, May 20, 2019.
Programs
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Mathematica
f[n_]:=f[n]=n*EulerPhi[n] T={};Do[If[f[n]<=200,T=Append[T,f[n]]],{n,1,200}]; tab={};Do[r=0;Do[If[f[k]>2n/3,Goto[cc]];Do[If[f[m]
Comments