

A321613


Partial products of the unitary totient function (A047994): a(n) = Product_{k=1..n} uphi(k).


1



1, 1, 2, 6, 24, 48, 288, 2016, 16128, 64512, 645120, 3870720, 46448640, 278691840, 2229534720, 33443020800, 535088332800, 4280706662400, 77052719923200, 924632639078400, 11095591668940800, 110955916689408000, 2441030167166976000, 34174422340337664000
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OFFSET

1,3


COMMENTS

a(n) is also the determinant of the symmetric n X n matrix M defined by M(i,j) = ugcd(i,j) for 1 <= i,j <= n, where ugcd(i,j) in the greatest common unitary divisor of i and j (A165430).


LINKS



EXAMPLE

a(4) = uphi(1) * uphi(2) * uphi(3) * uphi(4) = 1 * 1 * 2 * 3 = 6.


MATHEMATICA

uphi[1] = 1; uphi[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); FoldList[ Times, uphi /@ Range[50]]


PROG

(PARI) uphi(n) = my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]1); \\ A047994


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



