A373320 Numbers k such that phi(k)/k^2 < phi(m)/m^2 for all m < k, where phi is the Euler totient function (A000010).

1, 2, 3, 4, 6, 10, 12, 18, 24, 30, 42, 54, 60, 78, 84, 90, 114, 120, 150, 168, 180, 210, 270, 294, 300, 330, 390, 420, 510, 546, 570, 630, 750, 780, 840, 990, 1050, 1170, 1260, 1470, 1650, 1680, 1890, 2100, 2310, 2730, 3150, 3360, 3570, 3990, 4290, 4410, 4620

Offset: 1

Author

Amiram Eldar, Jun 01 2024

Keywords

• nonn

Comments

First differs from A330006 at n = 52: a(52) = 4410 is not a term of A330006. The first term of A330006 that is not in this sequence is A330006(127) = 166530.

Numbers are less likely to be unitary divisors than any smaller number, i.e., numbers k such that the asymptotic density of numbers that are unitarily divided by k (A373318(k)/A373319(k)) is lower than the corresponding density of all m < k.

The numbers k such that phi(k)/k < phi(m)/m for all m < k are the primorial numbers (A002110).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..670

Crossrefs

Cf. A000010, A002110, A330006, A373318, A373319.

Programs

Mathematica

seq[kmax_] := Module[{rm = 2, r, s = {}}, Do[If[(r = EulerPhi[k]/k^2) < rm, rm = r; AppendTo[s, k]], {k, 1, kmax}]; s]; seq[5000]

PARI

lista(kmax) = {my(rm = 2, r); for(k = 1, kmax, r = eulerphi(k)/k^2; if(r < rm, rm = r; print1(k, ", ")));}