A289828 a(n) is the least k such that phi(k) = n*phi(n).

1, 3, 7, 15, 25, 13, 43, 51, 81, 41, 121, 65, 157, 129, 143, 255, 289, 109, 361, 187, 301, 253, 529, 193, 625, 313, 487, 337, 841, 241, 961, 771, 661, 685, 899, 433, 1369, 1083, 937, 641, 1681, 551, 1849, 881, 1147, 1013, 2209, 769, 2401, 1111, 1751, 1249, 2809, 1141, 2323, 1469, 2053, 1711

Offset: 1

Author

Altug Alkan, Aug 13 2017

Keywords

• nonn
• easy

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000010, A002618, A015126.

Programs

Mathematica

With[{s = EulerPhi /@ Range[10^4]}, Table[First@ FirstPosition[s, n EulerPhi@ n], {n, 58}]] (* Michael De Vlieger, Aug 14 2017 *)

PARI

a(n) = my(k=1); while(1, if(eulerphi(k)==n*eulerphi(n), return(k)); k++) \\ Felix Fröhlich, Aug 14 2017

PARI

a(n) = invphiMin(n * eulerphi(n)); \\ Amiram Eldar, Nov 15 2024, using Max Alekseyev's invphi.gp

Formula

a(n) = A015126(n^2).

n^2/log log n << a(n) <= n^2. More specifically (on the lower bound), a(n) > n^2(e^-gamma + o(1))/log log n. - Charles R Greathouse IV, Aug 14 2017