A266268 Numbers n such that phi(n) = 3*phi(n-1).

7, 13, 19, 37, 73, 91, 97, 109, 163, 193, 433, 487, 577, 703, 769, 793, 925, 1153, 1297, 1459, 2593, 2917, 3457, 3889, 4699, 5551, 6697, 7999, 8701, 10369, 10591, 11803, 12289, 16471, 17497, 18433, 33251, 39367, 52489, 56791, 79249, 124357, 127927, 137899

Offset: 1

Author

Jaroslav Krizek, Dec 26 2015

Keywords

• nonn

Comments

Prime terms are in A058383.

See A266276(n) = the smallest numbers k such that phi(k) = n * phi(k-1) for n >=1: 2, 3, 7, 1261, 11242771, ...

Number of terms < 10^k: 1, 7, 17, 29, 41, 86, 205, 446, 1001, 2295, ..., . - Robert G. Wilson v, Jan 24 2016

All terms are == +-1 (mod 6) but mostly 1 (> 95%). - Robert G. Wilson v, Jan 24 2016

Examples

			19 is in the sequence because phi(19) = 18 = 3*phi(18) = 3*6.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..2467 (first 405 terms from G. C. Greubel)

Crossrefs

Cf. A000010, A058383, A171271 (numbers n such that phi(n) = 2*phi(n-1)), A266276.

Programs

Magma

[n: n in [2..2*10^5] | EulerPhi(n) eq 3*EulerPhi(n-1)]; // Vincenzo Librandi, Dec 26 2015

Mathematica

Select[Range[5000], EulerPhi[ # ]==3*EulerPhi[ #-1]&] (* G. C. Greubel, Dec 26 2015 *)

PARI

isok(n) = eulerphi(n) == 3*eulerphi(n-1); \\ Michel Marcus, Dec 27 2015

PARI

lista(nn) = for(n=1, nn, if(eulerphi(n) == 3*eulerphi(n-1), print1(n, ", "))); \\ Altug Alkan, Jan 24 2016

Formula

a(n) = A067143(n) + 1.