A074853 Numbers k not in A065036 but such that tau(k) = omega(k)^3.

900, 1764, 4356, 4900, 6084, 7560, 10404, 11025, 11880, 12100, 12996, 13440, 14040, 16632, 16900, 18360, 19044, 19656, 20520, 21000, 21120, 23716, 24840, 24960, 25704, 27225, 28728, 28900, 29568, 30276, 30888, 31320, 32640, 33000, 33124, 33480, 34596, 34776, 34944

Offset: 1

Author

Benoit Cloitre, Sep 10 2002

Keywords

• nonn

Comments

If k is in A065036 tau(k) = omega(k)^3, since k = p^3*q and there are 8 divisors of k: 1, p, q, p^2, p^3, p*q, p^2*q, p^3*q while omega(k)^3 = 2^3 = 8.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A001221, A065036.

Programs

Mathematica

q[k_] := Module[{e = Sort[FactorInteger[k][[;;, 2]]]}, e != {1, 3} && Times @@ (e+1) == Length[e]^3]; Select[Range[35000], q] (* Amiram Eldar, Apr 19 2025 *)

PARI

is(n)=my(f=factor(n)); numdiv(f)==omega(f)^3 && f[,2]!=[3,1]~ && f[,2]!=[1,3]~ \\ Charles R Greathouse IV, Oct 16 2015