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%I #13 Sep 08 2022 08:46:21
%S 1,4,6,96,10,3456,14,24576,486,16000,22,859963392,26,43904,54000,
%T 125829120,34,9795520512,38,18432000000,148176,170368,46,
%U 584325558976905216,3750,281216,1417176,138784407552,58,80621568000000000,62,24739011624960,574992,628864
%N a(n) = Product_{d|n} (tau(d)*pod(d)) where tau(k) = the number of divisors of k (A000005) and pod(k) = the product of the divisors of k (A007955).
%C n divides a(n) for all n.
%F a(n) = Product_{d|n} tau(d) * Product_{d|n} pod(d) = A211776(n) * A266265(n).
%F a(p) = 2p for p = primes (A000040).
%e a(6) = (tau(1)*pod(1)) * (tau(2)*pod(2)) * (tau(3)*pod(3)) * (tau(6)*pod(6)) = (1*1) * (2*2) * (2*3) * (4*36) = 3456.
%o (Magma) [&*[# [c: c in Divisors(d)] * &*[c: c in Divisors(d)]: d in Divisors(n)]: n in [1..100]]
%o (PARI) a(n) = my(d=divisors(n)); prod(k=1, #d, my(dd=divisors(d[k])); #dd*vecprod(dd)); \\ _Michel Marcus_, Apr 25 2019
%Y Cf. A000005, A007955, A307100.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Apr 25 2019
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