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A287800
Numbers n such that phi(n) * tau(n) divides n^2, but neither tau(n) nor phi(n) divides n.
1
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
KEYWORD
nonn
AUTHOR
Bernard Schott, Jun 01 2017
STATUS
approved