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A280583 a(n) = product of divisors of the number of divisors of n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
Sequence in context: A345281 A338319 A369748 * A177047 A339665 A334490
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jan 07 2017
STATUS
approved

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Last modified June 12 10:35 EDT 2024. Contains 373331 sequences. (Running on oeis4.)