%I #14 Sep 15 2024 02:39:54

%S 1,6,10,12,18,20,24,30,36,42,60,66,70,78,84,90,102,105,110,114,120,

%T 126,130,132,138,140,150,154,156,165,168,170,174,180,182,186,190,195,

%U 198,204,210,220,222,228,230,231,234,238,240,246,252,255,258,260,264,266

%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="/A110085/b110085.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[300], q] (* _Amiram Eldar_, Sep 15 2024 *)

%o (PARI) is(n)=sigma(n)-eulerphi(n)<numdiv(n)^omega(n) \\ _Charles R Greathouse IV_, Feb 14 2013

%o (Haskell)

%o a110085 n = a110085_list !! (n-1)

%o a110085_list = filter (\x -> a051612 x < a110088 x) [1..]

%o -- _Reinhard Zumkeller_, Aug 05 2014

%Y Intersection of A018252 and A110086

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

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Jul 11 2005