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

Author

Benoit Cloitre, Apr 13 2002

Keywords

• easy
• nonn

Comments

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

Links

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

Crossrefs

Composite numbers in A020491.

Cf. A002144, A046388.

Programs

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 *)

PARI

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