|
|
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
|
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|