A373320 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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

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]

PROG

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

CROSSREFS

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

Sequence in context: A249685 A343731 A181312 * A330006 A288784 A322164

Adjacent sequences: A373317 A373318 A373319 * A373321 A373322 A373323

KEYWORD

nonn

AUTHOR

Amiram Eldar, Jun 01 2024

STATUS

approved