A110087 - OEIS

%I #17 Sep 15 2024 02:40:38

%S 4,8,9,14,16,21,22,25,26,27,28,32,33,34,35,38,39,40,44,45,46,48,49,50,

%T 51,52,54,55,56,57,58,62,63,64,65,68,69,72,74,75,76,77,80,81,82,85,86,

%U 87,88,91,92,93,94,95,96,98,99,100,104,106,108,111,112,115,116,117,118

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

%H Reinhard Zumkeller, <a href="/A110087/b110087.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%o (PARI) is(n)=sigma(n)-eulerphi(n)>numdiv(n)^omega(n) \\ _Charles R Greathouse IV_, Feb 19 2013

%o (Haskell)

%o a110087 n = a110087_list !! (n-1)

%o a110087_list = filter (\x -> a051612 x > a110088 x) [1..]

%o -- _Reinhard Zumkeller_, Aug 05 2014

%Y Complement of A110086.

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

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jul 11 2005