A067573 Numbers k > 1 such that sigma(phi(k))/sigma(k) > sigma(phi(j))/sigma(j) for all 1 < j < k.

2, 3, 5, 7, 13, 31, 37, 61, 181, 241, 421, 1009, 1201, 1321, 1801, 2161, 2521, 7561, 12601, 15121, 30241, 55441, 110881, 278263, 332641, 555911, 666917, 722473, 1443853, 2165407, 3607403, 4324321, 7212581, 8654539, 10817761, 21631147, 36768847, 43243201, 61276871

Offset: 1

Author

Robert G. Wilson v, Jan 30 2002

Keywords

• nonn

Comments

Without the restrictions k > 1 and j > 1, 1 will be a term instead of 2 and 3. - Amiram Eldar, Apr 16 2024

Links

• Amiram Eldar, Table of n, a(n) for n = 1..53

Crossrefs

Cf. A000010 (phi), A000203 (sigma), A062402.

Programs

Mathematica

a = 0; Do[b = DivisorSigma[1, EulerPhi[n]]/DivisorSigma[1, n]; If[b > a, a = b; Print[n]], {n, 2, 10^7}]

PARI

lista(kmax) = {my(rm = 0, f); for(k = 2, kmax, f = factor(k); r = sigma(eulerphi(f)) / sigma(f); if(r > rm, rm = r; print1(k, ", ")));} \\ Amiram Eldar, Apr 16 2024

Extensions

a(37)-a(39) added and name corrected by Amiram Eldar, Apr 16 2024