A166142 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

LINKS

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

FORMULA

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

EXAMPLE

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

PROG

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

CROSSREFS

Cf. A080304, A166141, A014963.

Sequence in context: A080304 A340677 A340679 * A290479 A304404 A290480

Adjacent sequences: A166139 A166140 A166141 * A166143 A166144 A166145

KEYWORD

nonn

AUTHOR

Mats Granvik, Oct 08 2009

EXTENSIONS

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

STATUS

approved