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A053139 a(n) = phi(n) - mu(n). 1
0, 2, 3, 2, 5, 1, 7, 4, 6, 3, 11, 4, 13, 5, 7, 8, 17, 6, 19, 8, 11, 9, 23, 8, 20, 11, 18, 12, 29, 9, 31, 16, 19, 15, 23, 12, 37, 17, 23, 16, 41, 13, 43, 20, 24, 21, 47, 16, 42, 20, 31, 24, 53, 18, 39, 24, 35, 27, 59, 16, 61, 29, 36, 32, 47, 21, 67, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Robert P. Schneider, A golden product identity for e, Mathematics Magazine, Vol. 87, No. 2 (2014), pp. 132-134.
FORMULA
a(n) = n if and only if n is a prime.
Product_{n>=1} (1 - 1/phi^n)^(-a(n)/n) = e, where phi is the golden ratio (A001622) (Schneider, 2014). - Amiram Eldar, Jun 11 2022
MATHEMATICA
a[ n_] := EulerPhi @ n - MoebiusMu @ n; Table[a[n], {n, 70}] (* Michael Somos, Jul 19 2011 *)
PROG
(PARI) {a(n) = if( n==0, 0, eulerphi( n) - moebius( n))} /* Michael Somos, Jul 19 2011 */
(Magma) [EulerPhi(n) - MoebiusMu(n): n in [1..100]]; // G. C. Greubel, Sep 03 2018
CROSSREFS
Sequence in context: A332424 A293212 A157449 * A127705 A124386 A098668
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 25 2000
STATUS
approved

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Last modified March 19 06:05 EDT 2024. Contains 370952 sequences. (Running on oeis4.)