cp's OEIS Frontend

A110086 Numbers k such that sigma(k) - phi(k) <= tau(k)^omega(k), where sigma = A000203, phi = A000010, tau = A000005 and omega = A001221.

%I A110086 #15 Sep 15 2024 02:40:15
%S A110086 1,2,3,5,6,7,10,11,12,13,15,17,18,19,20,23,24,29,30,31,36,37,41,42,43,
%T A110086 47,53,59,60,61,66,67,70,71,73,78,79,83,84,89,90,97,101,102,103,105,
%U A110086 107,109,110,113,114,120,126,127,130,131,132,137,138,139,140,149,150,151
%N A110086 Numbers k such that sigma(k) - phi(k) <= tau(k)^omega(k), where sigma = A000203, phi = A000010, tau = A000005 and omega = A001221.
%H A110086 Charles R Greathouse IV, <a href="/A110086/b110086.txt">Table of n, a(n) for n = 1..10000</a>
%F A110086 A051612(a(n)) <= A110088(a(n)).
%t A110086 q[k_] := DivisorSigma[1, k] - EulerPhi[k] <= DivisorSigma[0, k]^PrimeNu[k]; Select[Range[160], q] (* _Amiram Eldar_, Sep 15 2024 *)
%o A110086 (PARI) is(n)=sigma(n)-eulerphi(n)<=numdiv(n)^omega(n) \\ _Charles R Greathouse IV_, Feb 14 2013
%o A110086 (Haskell)
%o A110086 a110086 n = a110086_list !! (n-1)
%o A110086 a110086_list = filter (\x -> a051612 x <= a110088 x) [1..]
%o A110086 -- _Reinhard Zumkeller_, Aug 05 2014
%Y A110086 Union of A000040 and A110085.
%Y A110086 Complement of A110086.
%Y A110086 Cf. A000005, A000010, A000203, A001221, A051612, A110088, A240960 (subsequence).
%K A110086 nonn
%O A110086 1,2
%A A110086 _Reinhard Zumkeller_, Jul 11 2005