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

Author

Torlach Rush, Jan 10 2019

Keywords

• nonn

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.

Examples

			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).
		

Links

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

Crossrefs

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

Cf. A001494, A033950, A046692.

Programs

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 *)

PARI

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

Extensions

Corrected and extended by Michel Marcus, Jan 16 2019