A359964 Refactorable numbers (A033950) having more divisors than all smaller refactorable numbers.

1, 2, 8, 12, 24, 36, 60, 180, 240, 360, 720, 1260, 1680, 3360, 5040, 10080, 15120, 20160, 25200, 30240, 55440, 100800, 110880, 221760, 277200, 443520, 665280, 720720, 1108800, 1441440, 2494800, 2882880, 3603600, 5765760, 8648640, 12972960, 14414400, 25945920, 28828800

Offset: 1

Author

Amiram Eldar, Jan 20 2023

Keywords

• nonn

Comments

The corresponding numbers of divisors are 1, 2, 4, 6, 8, 9, 12, 18, 20, 24, ... .

This sequence if infinite since there are refactorable numbers with arbitrarily large number of divisors. E.g., for any prime p, p^(p-1) is a refactorable number with p divisors.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..60

Crossrefs

Subsequence of A033950.

Cf. A000005, A073904, A110821.

Similar sequences: A002182, A335317, A356078, A359963.

Programs

Mathematica

seq[nmax_] := Module[{s = {}, dm = 0, d}, Do[d = DivisorSigma[0, n]; If[d > dm && Divisible[n, d], dm = d; AppendTo[s, n]], {n, 1, nmax}]; s]; seq[10^6]

PARI

lista(nmax) = {my(dm = 0, d); for(n = 1, nmax, d = numdiv(n); if(d > dm && n%d == 0, dm = d; print1(n, ", "))); }