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A280581 a(n) = the product of divisors of sum of divisors of n.

%I A280581 #23 Jun 26 2022 02:15:55
%S A280581 1,3,8,7,36,1728,64,225,13,5832,1728,21952,196,331776,331776,31,5832,
%T A280581 1521,8000,3111696,32768,10077696,331776,46656000000,31,3111696,
%U A280581 2560000,9834496,810000,139314069504,32768,250047,254803968,8503056,254803968,8281,1444
%N A280581 a(n) = the product of divisors of sum of divisors of n.
%C A280581 a(n) < A007955(n) for numbers n in A219364.
%C A280581 a(n) | A007955(n) for numbers n in A219363.
%C A280581 A007955(n) | a(n) for numbers n in A219362.
%C A280581 n | a(n) for numbers n in A175200.
%H A280581 Antti Karttunen, <a href="/A280581/b280581.txt">Table of n, a(n) for n = 1..1024</a>
%H A280581 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A280581 a(n) = A007955(A000203(n)).
%e A280581 For n = 5; a(n) = product of divisors of sigma(5) = 1*2*3*6 = 36.
%t A280581 Table[Times @@ Divisors@ DivisorSigma[1, n], {n, 37}] (* _Michael De Vlieger_, Jan 06 2017 *)
%t A280581 a[n_] := (s = DivisorSigma[1, n])^(DivisorSigma[0, s]/2); Array[a, 40] (* _Amiram Eldar_, Jun 26 2022 *)
%o A280581 (Magma) [&*[d: d in Divisors(SumOfDivisors(n))]: n in [1..100]]
%o A280581 (PARI) a(n) = my(k = 1); fordiv(sigma(n), d, k*=d); k; \\ _Michel Marcus_, Jan 06 2017
%o A280581 (Python)
%o A280581 from math import isqrt
%o A280581 from sympy import divisor_count, divisor_sigma
%o A280581 def A280581(n): return (lambda m:isqrt(m)**c if (c:=divisor_count(m)) & 1 else m**(c//2))(divisor_sigma(n)) # _Chai Wah Wu_, Jun 25 2022
%Y A280581 Cf. A000203, A007955, A219362, A219363, A219364, A280582.
%K A280581 nonn
%O A280581 1,2
%A A280581 _Jaroslav Krizek_, Jan 05 2017