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A067911 Product of GCD(k,n) for 1 <= k <= n. 7
1, 2, 3, 8, 5, 72, 7, 128, 81, 800, 11, 41472, 13, 6272, 30375, 32768, 17, 3359232, 19, 20480000, 750141, 247808, 23, 13759414272, 15625, 1384448, 1594323, 5035261952, 29, 30233088000000, 31, 2147483648, 235782657, 37879808 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

T. D. Noe, Table of n, a(n) for n=1..500

L. Toth, A survey of gcd-sum functions, J. Int. Seq. 13 (2010) # 10.8.1

FORMULA

a(n) = Product_{ d divides n } d^phi(n/d). - Vladeta Jovovic, Mar 08 2004

a(n) = n*A051190(n). - Peter Luschny, Apr 07 2013

MAPLE

with(numtheory): a := n -> mul(d^phi(n/d), d = divisors(n)):

seq(a(i), i = 1..34); # Peter Luschny, Apr 07 2013

PROG

(Sage)

A067911 = lambda n: mul(gcd(n, i) for i in range(n))

[A067911(n) for n in (1..34)] # Peter Luschny, Apr 07 2013

(PARI) a(n) = prod(k=1, n, gcd(k, n)); \\ Michel Marcus, Aug 23 2016

CROSSREFS

Cf. A051190, A051696.

In A018804 the product is replaced by sum.

Product of terms in n-th row of A050873.

Sequence in context: A112283 A136182 A170911 * A243103 A051696 A066570

Adjacent sequences:  A067908 A067909 A067910 * A067912 A067913 A067914

KEYWORD

nonn

AUTHOR

Sharon Sela (sharonsela(AT)hotmail.com), Mar 10 2002

EXTENSIONS

Extended and edited by John W. Layman, Mar 14 2002

STATUS

approved

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Last modified August 20 13:04 EDT 2017. Contains 290835 sequences.