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

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%I A280583 #19 Jun 25 2022 21:54:28
%S A280583 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,
%T A280583 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,
%U A280583 1728,2,8,36,7,8,64,2,36,8,64,2,1728,2,8,36,36,8
%N A280583 a(n) = product of divisors of the number of divisors of n.
%H A280583 Antti Karttunen, <a href="/A280583/b280583.txt">Table of n, a(n) for n = 1..10000</a>
%F A280583 a(n) = A007955(A000005(n)).
%F A280583 a(p) = 2 for p = primes (A000040).
%F A280583 a(n) = 3 for squares of primes (A001248).
%e A280583 For n = 6; a(n) = product of divisors (tau(6)) = 1*2*4 = 8.
%t A280583 Table[Times@@Divisors[DivisorSigma[0,n]],{n,80}] (* _Harvey P. Dale_, Dec 04 2021 *)
%o A280583 (Magma) [&*[d: d in Divisors(#[d: d in Divisors(n)])]: n in [1..100]]
%o A280583 (Python)
%o A280583 from math import isqrt
%o A280583 from sympy import divisor_count
%o A280583 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
%Y A280583 Cf. A000005, A000040, A001248, A007955, A010553, A062069.
%K A280583 nonn
%O A280583 1,2
%A A280583 _Jaroslav Krizek_, Jan 07 2017