A287800 Numbers n such that phi(n) * tau(n) divides n^2, but neither tau(n) nor phi(n) divides n.

900, 2400, 3840, 6480, 7200, 11520, 13056, 39168, 42240, 79200, 83232, 96000, 126720, 145200, 153600, 157440, 174240, 195840, 207360, 288000, 300000, 317520, 326592, 387840, 435600, 460800, 472320, 480000, 900000, 971520, 1056000, 1161600, 1163520, 1228800, 1440000

Offset: 1

Author

Bernard Schott, Jun 01 2017

Keywords

• nonn

Comments

The GCD of the first 43 terms is 12. The GCD of the first 166 terms is 4. The GCD of a(2) through a(166) is 16. - David A. Corneth, Jun 01 2017

Examples

			For n = 900, tau(900) = 27, phi(900) = 240 and 900^2/(27 * 240) = 125, but 900/27 = 33.33333 and 900/240 = 3.75.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..780 (terms below 10^10)

Crossrefs

Cf. A000005, A000010, A007694, A033950, A235353.

Programs

Magma

[k:k in [1..1500000]| k^2 mod (EulerPhi(k) *NumberOfDivisors(k)) eq 0 and (k mod  EulerPhi(k) ne 0) and (k mod NumberOfDivisors(k) ne 0)]; // Marius A. Burtea, Dec 30 2019

Maple

for n from 1 to 100000 do p(n):=n^2/(tau(n)*phi(n));
if p(n)=floor(p(n)) and n/tau(n)<>floor(n/tau(n)) and n/phi(n)<>floor(n/phi(n)) then print(n,p(n),phi(n),tau(n)) else fi; od:

Mathematica

Select[Range[10^6], Function[n, And[Divisible[n^2, #1 #2], NoneTrue[{#1, #2}, Divisible[n, #] &]] & @@ {DivisorSigma[0, n], EulerPhi[n]}]] (* Michael De Vlieger, Jun 01 2017 *)

PARI

is(n) = n^2 % (numdiv(n)*eulerphi(n)) == 0 && n % numdiv(n) != 0 && n % eulerphi(n) % n!=0 \\ David A. Corneth, Jun 01 2017