A065393 Sigma(phi(m)) - phi(sigma(m)) is increasing at these values of m.

3, 5, 7, 11, 13, 17, 19, 29, 31, 37, 41, 53, 61, 73, 95, 97, 109, 127, 143, 157, 181, 209, 241, 287, 313, 323, 337, 377, 403, 407, 421, 473, 527, 533, 541, 589, 601, 661, 713, 731, 757, 779, 899, 1009, 1073, 1147, 1159, 1199, 1271, 1321, 1333, 1349, 1517

Offset: 1

Author

Labos Elemer, Nov 05 2001

Keywords

• nonn

Comments

First composite number is the 15th term, 95. [Corrected by Jacob Vecht, Jul 28 2020]

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2000 (terms 1..500 from Harry J. Smith)

Crossrefs

Cf. A000010, A000203, A065394, A065395.

Programs

Mathematica

a = 0; s = 0; Do[s = DivisorSigma[1, EulerPhi[n]] - EulerPhi[DivisorSigma[1, n]]; If[s>a, a = s; Print[n]], {n, 1, 10000}]
DeleteDuplicates[Table[{m,DivisorSigma[1,EulerPhi[m]]-EulerPhi[DivisorSigma[1,m]]},{m,1600}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* Harvey P. Dale, Aug 02 2023 *)

PARI

{ n=r=0; for (m=1, 10^9, x=sigma(eulerphi(m)) - eulerphi(sigma(m)); if (x > r, r=x; write("b065393.txt", n++, " ", m); if (n==500, return)) ) } \\ Harry J. Smith, Oct 18 2009