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

1,2

Links

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

Formula

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

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A345281 A338319 A369748 * A177047 A339665 A334490

Adjacent sequences: A280580 A280581 A280582 * A280584 A280585 A280586

Keyword

nonn

Author

Jaroslav Krizek, Jan 07 2017

Status

approved