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%I #33 Apr 14 2021 22:24:54
%S 1,3,9,54,162,1458,4374,43740,262440,2361960,7085880,127545840,
%T 382637520,3443737680,30993639120,464904586800,1394713760400,
%U 25104847687200,75314543061600,1355661775108800,12200955975979200,109808603783812800,329425811351438400,9882774340543152000,59296646043258912000,533669814389330208000,5336698143893302080000,96060566590079437440000,288181699770238312320000,7780905893796434432640000
%N Partial products of A007425.
%C Partial products of the number of ordered factorizations of n as a product of 3 terms.
%C a(n) is also the determinant of the symmetric n X n matrix M defined by M(i,j) = d_4(gcd(i,j)) for 1 <= i,j <= n, where d_4(n) = A007426(n). - _Enrique Pérez Herrero_, Jan 20 2013
%H Antal Bege, <a href="http://www.emis.de/journals/AUSM/C1-1/MATH1-4.PDF">Hadamard product of GCD matrices</a>, Acta Univ. Sapientiae, Mathematica, 1, 1 (2009) 43-49.
%F a(n) = Product_{i=1..n} A007425(i).
%F a(n) = Product_{prime p<=n} Product_{k=1..floor(log_p(n))} (1 + 2/k)^floor(n/p^k). - _Ridouane Oudra_, Mar 23 2021
%e a(8) = 1 * 3 * 3 * 6 * 3 * 9 * 3 * 10 = 43740 = 2^2 * 3^7 * 5.
%t Table[Product[Sum[DivisorSigma[0, d], {d, Divisors[k]}], {k, 1, n}], {n, 1, 30}] (* _Vaclav Kotesovec_, Sep 03 2018 *)
%o (PARI) f(n) = sumdiv(n, k, numdiv(k)); \\ A007425
%o a(n) = prod(k=1, n, f(k)); \\ _Michel Marcus_, Mar 23 2021
%Y Cf. A000005, A007425, A007426, A061201 (partial sums), A127270, A143354.
%Y Cf. A066843.
%K nonn
%O 1,2
%A _Jonathan Vos Post_, Dec 03 2010
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