A262985 Number of ordered ways to write n as 2^x + phi(y^2) + z*(z+1)/2 with x, y and z positive integers, where phi(.) is Euler's totient function given by A000010.
0, 0, 0, 1, 1, 2, 2, 1, 3, 2, 5, 2, 5, 2, 5, 4, 4, 4, 5, 7, 3, 3, 5, 5, 8, 4, 5, 3, 5, 4, 8, 4, 3, 6, 5, 2, 9, 6, 8, 4, 5, 5, 8, 6, 8, 8, 4, 6, 8, 10, 7, 6, 7, 8, 9, 6, 7, 7, 12, 5, 9, 8, 6, 7, 12, 5, 9, 6, 9, 6, 11, 9, 11, 5, 6, 10, 8, 7, 9, 11, 5, 7, 7, 8, 7, 9, 8, 8, 9, 6, 7, 9, 7, 10, 9, 4, 6, 6, 7, 9
Offset: 1
Keywords
Examples
a(4) = 1 since 4 = 2 + phi(1^2) + 1*2/2. a(5) = 1 since 5 = 2 + phi(2^2) + 1*2/2. a(8) = 1 since 8 = 2^2 + phi(1^2) + 2*3/2. a(36) = 2 since 36 = 2 + phi(3^2) + 7*8/2 = 2^5 + phi(1^2) + 2*3/2.
Links
- Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
f[n_]:=EulerPhi[n^2] TQ[n_]:=n>0&&IntegerQ[Sqrt[8n+1]] Do[r=0;Do[If[f[x]>=n,Goto[aa]];Do[If[TQ[n-f[x]-2^y],r=r+1], {y,1,Log[2,n-f[x]]}]; Label[aa];Continue,{x,1,n}];Print[n," ",r];Continue,{n,1,100}]
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