A110087 Numbers k such that sigma(k) - phi(k) > tau(k)^omega(k), where sigma = A000203, phi = A000010, tau = A000005 and omega = A001221.

4, 8, 9, 14, 16, 21, 22, 25, 26, 27, 28, 32, 33, 34, 35, 38, 39, 40, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 62, 63, 64, 65, 68, 69, 72, 74, 75, 76, 77, 80, 81, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 98, 99, 100, 104, 106, 108, 111, 112, 115, 116, 117, 118

Offset

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Formula

A051612(a(n)) > A110088(a(n)).

Mathematica

q[k_] := DivisorSigma[1, k] - EulerPhi[k] > DivisorSigma[0, k]^PrimeNu[k]; Select[Range[120], q] (* Amiram Eldar, Sep 15 2024 *)

Prog

(PARI) is(n)=sigma(n)-eulerphi(n)>numdiv(n)^omega(n) \\ Charles R Greathouse IV, Feb 19 2013
(Haskell)
a110087 n = a110087_list !! (n-1)
a110087_list = filter (\x -> a051612 x > a110088 x) [1..]
-- Reinhard Zumkeller, Aug 05 2014

Crossrefs

Complement of A110086.

Cf. A000005, A000010, A000203, A001221, A051612, A110088.

Sequence in context: A112775 A107747 A121763 * A312830 A312831 A085711

Adjacent sequences: A110084 A110085 A110086 * A110088 A110089 A110090

Keyword

nonn

Author

Reinhard Zumkeller, Jul 11 2005

Status

approved