A322797 Powerful tau numbers.

1, 8, 9, 36, 72, 108, 128, 225, 288, 441, 625, 864, 972, 1089, 1152, 1521, 1800, 1944, 2000, 2025, 2601, 2700, 3249, 3456, 3528, 3600, 4500, 4761, 5000, 5292, 5625, 6561, 6912, 7569, 7776, 8100, 8649, 8712, 10000, 10800, 12168, 12321, 12348, 13068, 15129, 16000, 16200, 16641, 18000

Offset

1,2

Comments

If the largest exponent among the prime factors of a(n) does not exceed 2 then A046692(a(n)) = sqrt(a(n)), otherwise A046692(a(n)) = 0.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

1 is a term because A033950(1) = A001694(1) = 1.
8 is a term because A033950(8) divides A001694(3).
9 is a term because A033950(9) divides A001694(4).
36 is a term because A033950(36) divides A001694(9).

Mathematica

powtauQ[1] = True; powtauQ[n_] := Min[e = (Last /@ FactorInteger[n])] > 1 && Divisible[n, Times @@ (e + 1)]; Select[Range[18000], powtauQ] (* Amiram Eldar, Dec 30 2019 *)

Prog

(PARI) isok(n) = ispowerful(n) && ((n % numdiv(n)) == 0); \\ Michel Marcus, Jan 16 2019

Crossrefs

Intersection of A001694 (powerful numbers) and A033950 (tau numbers).

Cf. A001494, A033950, A046692.

Sequence in context: A041915 A036764 A129548 * A075079 A317379 A298665

Adjacent sequences: A322794 A322795 A322796 * A322798 A322799 A322800

Keyword

nonn

Author

Torlach Rush, Jan 10 2019

Extensions

Corrected and extended by Michel Marcus, Jan 16 2019

Status

approved