A280927 Odd numbers k such that phi(k) and cototient(k) have the same prime signature.

1735, 2469, 4341, 4569, 4989, 5469, 5637, 5961, 6879, 7149, 7407, 8675, 9969, 11569, 12949, 13057, 13089, 13707, 15829, 15969, 16407, 18597, 18969, 19959, 20109, 20487, 20721, 21081, 21309, 21729, 22107, 22221, 22513, 23469, 24355, 25269, 25617, 26305, 27021

Offset

1,1

Comments

46347 = 3*7*2207 is the least term that has 3 distinct prime factors.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

1735 is a term because phi(1735) = 1384 = 2^3 * 173 and cototient(1735) = 1735 - phi(1735) = 351 = 3^3 * 13.

Mathematica

Select[Range[5, 30000, 2], Sort @ FactorInteger[(phi = EulerPhi[#])][[;; , 2]] == Sort @ FactorInteger[# - phi][[;; , 2]] &] (* Amiram Eldar, Jan 02 2021 *)

Prog

(PARI) is(n) = vecsort(factor(eulerphi(n))[, 2]) == vecsort(factor(n-eulerphi(n))[, 2]) && n%2==1;

Crossrefs

Cf. A000010, A051953.

Sequence in context: A113701 A283385 A083606 * A095847 A253696 A253703

Adjacent sequences: A280924 A280925 A280926 * A280928 A280929 A280930

Keyword

nonn

Author

Altug Alkan, Jan 10 2017

Status

approved