A280583 a(n) = product of divisors of the number of divisors of n.

1, 2, 2, 3, 2, 8, 2, 8, 3, 8, 2, 36, 2, 8, 8, 5, 2, 36, 2, 36, 8, 8, 2, 64, 3, 8, 8, 36, 2, 64, 2, 36, 8, 8, 8, 27, 2, 8, 8, 64, 2, 64, 2, 36, 36, 8, 2, 100, 3, 36, 8, 36, 2, 64, 8, 64, 8, 8, 2, 1728, 2, 8, 36, 7, 8, 64, 2, 36, 8, 64, 2, 1728, 2, 8, 36, 36, 8

Offset: 1

Author

Jaroslav Krizek, Jan 07 2017

Keywords

• nonn

Examples

			For n = 6; a(n) = product of divisors (tau(6)) = 1*2*4 = 8.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000040, A001248, A007955, A010553, A062069.

Programs

Magma

[&*[d: d in Divisors(#[d: d in Divisors(n)])]: n in [1..100]]

Mathematica

Table[Times@@Divisors[DivisorSigma[0,n]],{n,80}] (* Harvey P. Dale, Dec 04 2021 *)

Python

from math import isqrt
from sympy import divisor_count
def A280583(n): return (lambda m:(isqrt(m) if (c:=divisor_count(m)) & 1 else 1)*m**(c//2))(divisor_count(n)) # Chai Wah Wu, Jun 25 2022

Formula

a(n) = A007955(A000005(n)).

a(p) = 2 for p = primes (A000040).

a(n) = 3 for squares of primes (A001248).