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EXAMPLE
| 1# d[n]=r[n] holds for {1,3,8,10,18,24,30}, see A020488;
2# d[n]=u[n] holds for {15,25};3# r[n]=u[n] holds for {61455};
4# n-u[n]=u[n] holds for {30,50}. No more cases below 10^7.
{n,d,r,u} values for 11 initial terms are as follows:
{1, 1, 1, 0}, {3, 2, 2, 0}, {8, 4, 4, 1}, {10, 4, 4, 3}, {15, 4, 8, 4}, {18, 6, 6, 7}{24, 8, 8, 9}, {25, 3, 20, 3}, {30, 8, 8, 15}, {50, 6, 20, 25}, {61455, 16, 30720, 30720}.
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MATHEMATICA
| Do[r=EulerPhi[n]; d=DivisorSigma[0, n]; u=n-r-d+1; If[Equal[d, r]||Equal[d, u]||Equal[r, u]||Equal[u, n-u], Print[n(*, {d, r, u}*)]], {n, 1, 10000000}]
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