A069237 Composite numbers k such that tau(k) divides phi(k), where tau(k) is the number of divisors of k and phi(k) the Euler totient function.

8, 9, 10, 15, 18, 21, 24, 26, 28, 30, 33, 34, 35, 39, 40, 45, 49, 51, 52, 55, 56, 57, 58, 63, 65, 69, 70, 72, 74, 76, 77, 78, 82, 84, 85, 87, 88, 90, 91, 93, 95, 98, 99, 102, 104, 105, 106, 108, 110, 111, 115, 117, 119, 120, 122, 123, 124, 125, 126, 128, 129, 130, 133

Offset

1,1

Comments

Includes A046388 and 2*A002144. - Robert Israel, Jan 05 2018

Links

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

Maple

filter:= n -> not isprime(n) and numtheory:-phi(n) mod numtheory:-tau(n)=0:
select(filter, [$4..1000]); # Robert Israel, Jan 05 2018

Mathematica

nn=200; Rest[Select[Complement[Range[nn], Prime[Range[PrimePi[nn]]]], Divisible[ EulerPhi[#], DivisorSigma[0, #]]&]] (* Harvey P. Dale, Mar 31 2011 *)

Prog

(PARI) isok(k) = if(k == 1 || isprime(k), 0, my(f = factor(k)); !(eulerphi(f) % numdiv(f))); \\ Amiram Eldar, Apr 19 2025

Crossrefs

Composite numbers in A020491.

Cf. A002144, A046388.

Sequence in context: A358674 A358675 A091417 * A334728 A070480 A135043

Adjacent sequences: A069234 A069235 A069236 * A069238 A069239 A069240

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 13 2002

Status

approved