A089693 Numbers k such that phi(k) = 2^bigomega(k).

1, 3, 10, 20, 30, 40, 60, 80, 120, 160, 240, 320, 480, 640, 960, 1280, 1920, 2560, 3840, 5120, 7680, 10240, 15360, 20480, 30720, 40960, 61440, 81920, 122880, 163840, 245760, 327680, 491520, 655360, 983040, 1310720, 1966080, 2621440, 3932160, 5242880, 7864320

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,2).

Formula

a(n) = 2*a(n-2) for n>5. - Harvey P. Dale, Mar 01 2012

From Enrique Pérez Herrero, Mar 28 2012: (Start)

For n > 2, A001222(a(n)) = 1 + floor(n/2).

For n > 1, a(2*n) = 5*2^n and a(2*n+1) = 15*2^(n-1). (End)

From Elmo R. Oliveira, Apr 26 2026: (Start)

a(n) = 10*A029744(n-2) for n > 2.

G.f.: x*(1 + 3*x + 8*x^2 + 14*x^3 + 10*x^4)/(1 - 2*x^2). (End)

Mathematica

Select[Range[100000], EulerPhi[#]==2^PrimeOmega[#]&] (* Harvey P. Dale, Mar 01 2012 *)
(* Alternative: *)
Join[{1, 3, 10}, LinearRecurrence[{0, 2}, {20, 30}, 20]] (* Harvey P. Dale, Mar 01 2012 *)

Crossrefs

Cf. A000010, A001222, A029744, A061142, A070004.

Sequence in context: A056789 A174476 A098645 * A194116 A208951 A299692

Adjacent sequences: A089690 A089691 A089692 * A089694 A089695 A089696

Keyword

nonn,easy

Author

Benoit Cloitre, Jan 06 2004

Extensions

More terms from Harvey P. Dale, Mar 01 2012

Status

approved