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

1,1

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

Links

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

Example

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.

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A074853 A162143 A258888 * A246887 A232556 A069096

Adjacent sequences: A287797 A287798 A287799 * A287801 A287802 A287803

Keyword

nonn

Author

Bernard Schott, Jun 01 2017

Status

approved