A015702 Numbers k where phi(k) + sigma(k) increases to a record value.

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, 120, 144, 168, 180, 210, 216, 240, 280, 288, 300, 324, 336, 360, 420, 480, 504, 540, 576, 600, 648, 660, 672, 720, 840, 960, 1008, 1080, 1200, 1260, 1440

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1288 (terms < 10^12)
• Richard K. Guy, Divisors and desires, Amer. Math. Monthly, 104 (1997), 359-360.

Crossrefs

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

Programs

Mathematica

seq = {}; sm = 0; s = 0; Do[s = EulerPhi[n] + DivisorSigma[1, n];
If[s > sm, sm = s; AppendTo[seq, n]], {n, 1, 1500}]; seq (* Amiram Eldar, Dec 05 2018 *)
DeleteDuplicates[Table[{n,EulerPhi[n]+DivisorSigma[1,n]},{n,1500}],GreaterEqual[ #1[[2]],#2[[2]]]&][[;;,1]] (* Harvey P. Dale, Mar 13 2023 *)

PARI

f(n)=eulerphi(n=factor(n))+sigma(n)
r=0;for(n=1,1e6,t=f(n); if(t>r,r=t; print1(n", "))) \\ Charles R Greathouse IV, Nov 27 2013