A332646 Numbers m with a divisor d such that d^tau(d) = m.

1, 4, 9, 25, 49, 64, 121, 169, 289, 361, 529, 729, 841, 961, 1296, 1369, 1681, 1849, 2209, 2809, 3481, 3721, 4096, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10000, 10201, 10609, 11449, 11881, 12769, 15625, 16129, 17161, 18769, 19321, 22201, 22801, 24649, 26569

Offset: 1

Author

Jaroslav Krizek, Feb 18 2020

Keywords

• nonn

Comments

Possible values for function n^tau(n) (A062758).

Supersequence of A189991 (numbers with prime factorization p^4*q^4; d = pq), A001248 (numbers with prime factorization p^2; d = p), A030516 (numbers with prime factorization p^6; d = p^2) and A280076.

Examples

			64 is a term because 4^3 = 64; 4 divides 64; tau(4) = 3.
		

Crossrefs

Cf. A000005, A001248, A030516, A062758, A189991, A280076.

Programs

Magma

[n: n in [1..100000] | #[d: d in Divisors(n) | d^NumberOfDivisors(d) eq n] ge 1];

Mathematica

divPowerQ[n_] := AnyTrue[Divisors[n], #^DivisorSigma[0, #] == n &]; Select[Range[27000], divPowerQ] (* Amiram Eldar, Feb 18 2020 *)

PARI

isok(m) = fordiv(m, d, if (d^numdiv(d) == m, return (1))); \\ Michel Marcus, Feb 18 2020