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A280583 a(n) = product of divisors of the number of divisors of n. 1

%I #19 Jun 25 2022 21:54:28

%S 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 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 1728,2,8,36,7,8,64,2,36,8,64,2,1728,2,8,36,36,8

%N a(n) = product of divisors of the number of divisors of n.

%H Antti Karttunen, <a href="/A280583/b280583.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

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

%t Table[Times@@Divisors[DivisorSigma[0,n]],{n,80}] (* _Harvey P. Dale_, Dec 04 2021 *)

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

%o (Python)

%o from math import isqrt

%o from sympy import divisor_count

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

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Jan 07 2017

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)