A280450 Smallest k > 2n+1 such that phi(k) = phi(2n+1).

4, 8, 9, 14, 22, 21, 16, 32, 27, 26, 46, 33, 38, 58, 62, 44, 39, 57, 45, 55, 49, 52, 94, 86, 64, 106, 75, 63, 118, 77, 74, 104, 134, 92, 142, 91, 82, 93, 158, 162, 166, 128, 116, 115, 95, 99, 111, 119, 122, 125, 206, 112, 214, 133, 117, 145, 178, 135, 153, 242

Offset: 1

Author

Thomas Ordowski, Jan 03 2017

Keywords

• nonn

Comments

All terms are composite.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A001274, A005384, A140141.

Programs

Maple

f:= n -> min(select(`>`,numtheory:-invphi(numtheory:-phi(2*n+1)),2*n+1)):
map(f, [$1..100]); # Robert Israel, Jan 03 2017

Mathematica

Table[k = 2 n + 2; While[EulerPhi@ k != #, k++] &@ EulerPhi[2 n + 1]; k, {n, 120}] (* Michael De Vlieger, Jan 03 2017 *)

PARI

a(n) = my(k=2*n+2); while(eulerphi(k)!=eulerphi(2*n+1), k++); k \\ Felix Fröhlich, Jan 05 2017

Formula

2n+1 < a(n) < 4n+3.

From Robert Israel, Jan 03 2017: (Start)

a(n)=2n+2 if and only if 2n+1 is in A001274.

If n > 3 is in A005384, then a(n)=4n+2. (End)