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A089692
a(n) = phi(2n)/2^omega(n).
1
1, 1, 1, 2, 2, 1, 3, 4, 3, 2, 5, 2, 6, 3, 2, 8, 8, 3, 9, 4, 3, 5, 11, 4, 10, 6, 9, 6, 14, 2, 15, 16, 5, 8, 6, 6, 18, 9, 6, 8, 20, 3, 21, 10, 6, 11, 23, 8, 21, 10, 8, 12, 26, 9, 10, 12, 9, 14, 29, 4, 30, 15, 9, 32, 12, 5, 33, 16, 11, 6, 35, 12, 36, 18, 10, 18, 15, 6, 39, 16, 27, 20, 41, 6, 16, 21
OFFSET
1,4
COMMENTS
Here omega(n) means the number of prime factors of n counted without multiplicity. - Harvey P. Dale, Dec 12 2012
LINKS
FORMULA
a(n) = A062570(n)/A034444(n).
Multiplicative with a(2^e) = 2^(e-1) and a(p^e) = (p^e-p^(e-1))/2 for an odd prime p. - Vladeta Jovovic, Jan 15 2004
a(n) = A000010(n)/2^A005087(n). - Michel Marcus, Jun 30 2023
MATHEMATICA
Table[EulerPhi[2n]/2^PrimeNu[n], {n, 90}] (* Harvey P. Dale, Dec 12 2012 *)
f[p_, e_] := If[p == 2, 2^(e-1), (p^e-p^(e-1))/2]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 09 2022 *)
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Benoit Cloitre, Jan 06 2004
STATUS
approved