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%I #9 Sep 08 2022 08:46:24
%S 1,6,12,336,30,31104,56,322560,4212,324000,132,84276412416,182,
%T 1580544,1944000,10239344640,306,2483164449792,380,6096384000000,
%U 9483264,13799808,552,1610547321930095001600,116250,31004064,122821920,108806975520768,870
%N a(n) = Product_{d|n} (sigma(d)*pod(d)) where sigma(k) = the sum of the divisors of k (A000203) 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} sigma(d) * Product_{d|n} pod(d) = A206032(n) * A266265(n).
%F a(p) = p*(p+1) for p = primes (A000040).
%e a(6) = (sigma(1)*pod(1)) * (sigma(2)*pod(2)) * (sigma(3)*pod(3)) * (sigma(6)*pod(6)) = (1*1) * (3*2) * (4*3) * (12*36) = 31104.
%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])); vecsum(dd)*vecprod(dd)); \\ _Michel Marcus_, Apr 25 2019
%Y Cf. A000203, A007955, A325029.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Apr 25 2019
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