A382326 Numbers with a record ratio of nontrivial divisors to prime factors (counted with multiplicity).

4, 6, 12, 24, 30, 60, 120, 180, 210, 360, 420, 840, 1260, 2310, 2520, 4620, 7560, 9240, 13860, 27720, 55440, 60060, 83160, 110880, 120120, 138600, 166320, 180180, 277200, 360360, 720720, 1081080, 1441440, 1801800, 2162160, 3063060, 3603600, 5405400, 6126120

Offset: 1

Author

Charles L. Hohn, Mar 21 2025

Keywords

• nonn

Comments

Numbers k that give a record value for A070824(k)/A001222(k).

Examples

			a(1) = 4: |{2}| / |{2, 2}| = 1/2.
a(2) = 6: |{2, 3}| / |{2, 3}| = 2/2.
a(3) = 12: |{2, 3, 4, 6}| / |{2, 2, 3}| = 4/3.
		

Crossrefs

Cf. A070824, A001222, A002182, A382325, A382327.

Subsequence of A025487.

Programs

PARI

my(mx=0); for(x=2, 10^5, my(f=factor(x), m=(numdiv(f)-2)/bigomega(f)); if(m>mx, mx=m; print1(x, ", ")))