A110085 Numbers k such that sigma(k) - phi(k) < tau(k)^omega(k), where sigma = A000203, phi = A000010, tau = A000005 and omega = A001221.

1, 6, 10, 12, 18, 20, 24, 30, 36, 42, 60, 66, 70, 78, 84, 90, 102, 105, 110, 114, 120, 126, 130, 132, 138, 140, 150, 154, 156, 165, 168, 170, 174, 180, 182, 186, 190, 195, 198, 204, 210, 220, 222, 228, 230, 231, 234, 238, 240, 246, 252, 255, 258, 260, 264, 266

Offset

1,2

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[300], q] (* Amiram Eldar, Sep 15 2024 *)

Prog

(PARI) is(n)=sigma(n)-eulerphi(n)<numdiv(n)^omega(n) \\ Charles R Greathouse IV, Feb 14 2013
(Haskell)
a110085 n = a110085_list !! (n-1)
a110085_list = filter (\x -> a051612 x < a110088 x) [1..]
-- Reinhard Zumkeller, Aug 05 2014

Crossrefs

Intersection of A018252 and A110086

Cf. A000005, A000010, A000203, A001221, A051612, A110087, A110088.

Sequence in context: A242100 A125592 A292431 * A315126 A315127 A231567

Adjacent sequences: A110082 A110083 A110084 * A110086 A110087 A110088

Keyword

nonn

Author

Reinhard Zumkeller, Jul 11 2005

Status

approved