A110192 Least k > n such that phi(k) = 2*phi(n), where phi is Euler's totient function.

3, 3, 5, 5, 15, 8, 13, 15, 13, 15, 25, 15, 35, 21, 17, 17, 51, 21, 37, 32, 35, 25, 69, 32, 41, 35, 37, 35, 87, 32, 61, 51, 41, 51, 65, 39, 73, 57, 65, 51, 123, 45, 129, 55, 65, 69, 141, 51, 129, 55, 85, 65, 159, 57, 123, 65, 73, 87, 177, 64, 143, 77, 73, 85, 97, 75, 161, 85

Offset: 1

Author

T. D. Noe, Jul 15 2005

Keywords

• nonn
• look

Links

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

Crossrefs

Cf. A000010, A110179.

Programs

Mathematica

Table[k=n+1; e=EulerPhi[n]; While[EulerPhi[k] != 2e, k++ ]; k, {n, 100}]

PARI

a(n) = vecmin(select(x -> x > n, invphi(2*eulerphi(n)))); \\ Amiram Eldar, Nov 05 2024, using Max Alekseyev's invphi.gp

Formula

a(n) = A110179(n) + n.