A331667 Numbers m with a divisor d such that tau(d)^d = m.

1, 4, 19683, 65536, 2176782336, 101559956668416, 7958661109946400884391936

Offset: 1

Author

Jaroslav Krizek, Feb 28 2020

Keywords

• nonn

Comments

Corresponding values of divisors d and tau(d) are 1, 2, 9, 8, 12, 18, 32, ..., and 1, 2, 3, 4, 6, 6, 6, ..., respectively.

a(8) = 2^144*3^72 = 12^72 is too large to be included in Data. - Giovanni Resta, Feb 28 2020

Examples

			19683 is a term because 3^9 = 19683; 9 divides 19683, tau(9) = 3.
		

Crossrefs

Cf. A236284 (tau(n)^n).

Cf. A000005, A332646.

Programs

Magma

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

Mathematica

seqQ[n_] := AnyTrue[Divisors[n], DivisorSigma[0, #]^# == n &]; Select[Range[70000], seqQ] (* Amiram Eldar, Feb 28 2020 *)

PARI

isok(m) = fordiv(m, d, if (numdiv(d)^d == m, return (1));); \\ Michel Marcus, Mar 07 2020

Extensions

More terms from Giovanni Resta, Feb 28 2020