A166142 Row products of A166141; Product of such divisors of n that are squarefree and have an even number of prime factors.

1, 1, 1, 1, 1, 6, 1, 1, 1, 10, 1, 6, 1, 14, 15, 1, 1, 6, 1, 10, 21, 22, 1, 6, 1, 26, 1, 14, 1, 900, 1, 1, 33, 34, 35, 6, 1, 38, 39, 10, 1, 1764, 1, 22, 15, 46, 1, 6, 1, 10, 51, 26, 1, 6, 55, 14, 57, 58, 1, 900, 1, 62, 21, 1, 65, 4356, 1, 34, 69, 4900, 1, 6, 1, 74, 15, 38, 77, 6084, 1, 10

Offset: 1

Author

Mats Granvik, Oct 08 2009

Keywords

• nonn

Examples

			For n = 30 = 2*3*5, all its divisors [1, 2, 3, 5, 6, 10, 15, 30] are squarefree, but only 1, 6, 10 and 15 have an even number of prime factors, thus a(30) = 1*6*10*15 = 900. - _Antti Karttunen_, Aug 06 2018
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A080304, A166141, A014963.

Programs

PARI

A166142(n) = { my(m=1); fordiv(n,d,m *= if(moebius(d) > 0,d,1)); (m); }; \\ Antti Karttunen, Aug 06 2018

Formula

a(n) = Product_{d|n} A080304(d). - Antti Karttunen, Aug 06 2018

Extensions

Alternative definition added to the name by Antti Karttunen, Aug 06 2018