A378315 Odd numbers k such that d(phi(k)) = phi(d(k)), where d=A000005 and phi=A000010.

1, 15230439315, 18887708385, 74989937295, 78103226565, 86031400455, 114958521405, 179883837315, 210096608085, 367588711035, 418094581905, 461441147895, 590648954805, 649146021615, 685787041485, 836850895335, 874197762165, 990695282031, 996070731201, 1002913997085, 1016370465201, 1029306324501, 1029869788311, 1039854060045, 1043905592457

Offset

1,2

Comments

For n > 1, we have A001222(a(n)) >= 9. The smallest a(n) with A001222(a(n)) = 9 is a(65) = 1244586078645.

Links

Max Alekseyev, Table of n, a(n) for n = 1..65

Tong Lingling et al., Find the smallest odd integer n>1 such that phi(tau(n)) = tau(phi(n)), MathOverflow, 2025.

zhouzixiang2004, DMOPC'21 Contest 10 P5 - Number Theory, DMOJ Monthly Open Programming Competition, 2021.

Crossrefs

Subsequence of A078148.

Cf. A000005, A000010, A033632.

Sequence in context: A186094 A023050 A233704 * A153432 A349324 A022241

Adjacent sequences: A378312 A378313 A378314 * A378316 A378317 A378318

Keyword

nonn,new

Author

Max Alekseyev, Jan 09 2025

Status

approved