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A029940 a(n) = Product_{d divides n} phi(d). 10
1, 1, 2, 2, 4, 4, 6, 8, 12, 16, 10, 32, 12, 36, 64, 64, 16, 144, 18, 256, 144, 100, 22, 1024, 80, 144, 216, 864, 28, 4096, 30, 1024, 400, 256, 576, 13824, 36, 324, 576, 16384, 40, 20736, 42, 4000, 9216, 484, 46, 131072, 252, 6400, 1024, 6912, 52, 46656, 1600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

J. R. Collis, On products of multiplicative functions, The Mathematical Gazette, Vol. 97, No. 539 (2013), pp. 263-264.

FORMULA

If n = Product_{i} p_i^e_i then a(n) = (sqrt(n) * Product_{i} (1 - 1/p_i)^(e_i/(e_i + 1))) ^ d(n), where d(n) is the number of divisors of n (Collis, 2013). - Amiram Eldar, Jun 16 2020

MAPLE

seq(mul(numtheory:-phi(i), i=numtheory:-divisors(n)), n=1..100); # Robert Israel, Nov 21 2014

MATHEMATICA

Table[Product[EulerPhi[i], {i, Divisors[n]}], {n, 100}] (* Carl Najafi, Sep 06 2011 *)

PROG

(PARI) a(n) = my(d = divisors(n)); prod(k=1, #d, eulerphi(d[k])); \\ Michel Marcus, Nov 21 2014

CROSSREFS

Cf. A000005, A000010.

Sequence in context: A264393 A094858 A327851 * A045674 A276065 A325253

Adjacent sequences:  A029937 A029938 A029939 * A029941 A029942 A029943

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Carl Najafi, Sep 06 2011

STATUS

approved

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Last modified September 29 21:59 EDT 2020. Contains 337432 sequences. (Running on oeis4.)