OFFSET
1,2
LINKS
T. D. Noe, Table of n, a(n) for n = 1..500
Johann Cigler, Some remarks on the power product expansion of the q-exponential series, arXiv:2006.06242 [math.CO], 2020.
Gottfried Helms, A dream of a (number-) sequence, 2007-2009.
L. Toth, A survey of gcd-sum functions, J. Int. Seq. 13 (2010) # 10.8.1.
FORMULA
a(n) = Product_{d|n} d^phi(n/d). - Vladeta Jovovic, Mar 08 2004
a(n) = n*A051190(n). - Peter Luschny, Apr 07 2013
a(n) = Product_{k=1..n} (n/gcd(n,k))^(phi(gcd(n,k))/phi(n/gcd(n,k))) where phi = A000010. - Richard L. Ollerton, Nov 07 2021
MAPLE
with(numtheory): a := n -> mul(d^phi(n/d), d = divisors(n)):
seq(a(i), i = 1..34); # Peter Luschny, Apr 07 2013
MATHEMATICA
a[n_] := Product[d^EulerPhi[n/d], {d, Divisors[n]}];
Array[a, 34] (* Jean-François Alcover, Jun 03 2019 *)
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
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