A359964 - OEIS

%I #12 Jan 23 2023 02:33:10

%S 1,2,8,12,24,36,60,180,240,360,720,1260,1680,3360,5040,10080,15120,

%T 20160,25200,30240,55440,100800,110880,221760,277200,443520,665280,

%U 720720,1108800,1441440,2494800,2882880,3603600,5765760,8648640,12972960,14414400,25945920,28828800

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

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

%C 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.

%H Amiram Eldar, <a href="/A359964/b359964.txt">Table of n, a(n) for n = 1..60</a>

%t 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]

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

%Y Subsequence of A033950.

%Y Cf. A000005, A073904, A110821.

%Y Similar sequences: A002182, A335317, A356078, A359963.

%K nonn

%O 1,2

%A _Amiram Eldar_, Jan 20 2023