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A175596 Partial products of A007425. 2
1, 3, 9, 54, 162, 1458, 4374, 43740, 262440, 2361960, 7085880, 127545840, 382637520, 3443737680, 30993639120, 464904586800, 1394713760400, 25104847687200, 75314543061600, 1355661775108800, 12200955975979200, 109808603783812800, 329425811351438400, 9882774340543152000, 59296646043258912000, 533669814389330208000, 5336698143893302080000, 96060566590079437440000, 288181699770238312320000, 7780905893796434432640000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Partial products of the number of ordered factorizations of n as a product of 3 terms.

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

LINKS

Table of n, a(n) for n=1..30.

Antal Bege, Hadamard product of GCD matrices, Acta Univ. Sapientiae, Mathematica, 1, 1 (2009) 43-49.

FORMULA

a(n) = Product_{i=1..n} A007425(i).

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

EXAMPLE

a(8) = 1 * 3 * 3 * 6 * 3 * 9 * 3 * 10 = 43740 = 2^2 * 3^7 * 5.

MATHEMATICA

Table[Product[Sum[DivisorSigma[0, d], {d, Divisors[k]}], {k, 1, n}], {n, 1, 30}] (* Vaclav Kotesovec, Sep 03 2018 *)

PROG

(PARI) f(n) = sumdiv(n, k, numdiv(k)); \\ A007425

a(n) = prod(k=1, n, f(k)); \\ Michel Marcus, Mar 23 2021

CROSSREFS

Cf. A000005, A007425, A007426, A061201 (partial sums), A127270, A143354.

Cf. A066843.

Sequence in context: A013341 A077795 A038496 * A261397 A238906 A212418

Adjacent sequences:  A175593 A175594 A175595 * A175597 A175598 A175599

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Dec 03 2010

STATUS

approved

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Last modified September 24 09:10 EDT 2021. Contains 347630 sequences. (Running on oeis4.)