A015702 - OEIS

%I #22 Mar 13 2023 09:52:20

%S 1,2,3,4,5,6,8,10,12,16,18,20,24,30,36,40,42,48,56,60,72,84,90,96,108,

%T 120,144,168,180,210,216,240,280,288,300,324,336,360,420,480,504,540,

%U 576,600,648,660,672,720,840,960,1008,1080,1200,1260,1440

%N Numbers n where phi(n) + sigma(n) increases.

%H Donovan Johnson, <a href="/A015702/b015702.txt">Table of n, a(n) for n = 1..1288</a> (terms < 10^12)

%H Richard K. Guy, <a href="http://www.jstor.org/stable/2974586">Divisors and desires</a>, Amer. Math. Monthly, 104 (1997), 359-360.

%t seq = {}; sm = 0; s = 0; Do[s = EulerPhi[n] + DivisorSigma[1, n];

%t If[s > sm, sm = s; AppendTo[seq, n]], {n, 1, 1500}]; seq (* _Amiram Eldar_, Dec 05 2018 *)

%t DeleteDuplicates[Table[{n,EulerPhi[n]+DivisorSigma[1,n]},{n,1500}],GreaterEqual[ #1[[2]],#2[[2]]]&][[;;,1]] (* _Harvey P. Dale_, Mar 13 2023 *)

%o (PARI) f(n)=eulerphi(n=factor(n))+sigma(n)

%o r=0;for(n=1,1e6,t=f(n); if(t>r,r=t; print1(n", "))) \\ _Charles R Greathouse IV_, Nov 27 2013

%Y Cf. A000203, A000010, A018892, A018894, A065387.

%K nonn

%O 1,2

%A _Robert G. Wilson v_