A306585 Start with n and find the LCM of n and A140635(n), and continue until a number m is reached such that A140635(m) = m.

1, 2, 6, 4, 120, 6, 840, 24, 36, 120, 83160, 12, 1081080, 840, 120, 16, 294053760, 36, 5587021440, 60, 840, 83160, 128501493120, 24, 900, 1081080, 7560, 2520, 93163582512000, 120, 2888071057872000, 10080, 83160, 294053760, 840, 36, 106858629141264000, 5587021440, 1081080, 120, 4381203794791824000

Offset

1,2

Comments

a(n) = n is a subsequence of minimal numbers A007416, i.e., when A140635(n) = n. It appears that p_n > log_2(sigma_0(a(p_n))) for all primes p_n, and that a(p_n) form an increasing subsequence satisfying a(k) < a(p_n) for all k < p_n. - Hartmut F. W. Hoft, Mar 14 2023

Links

Hartmut F. W. Hoft, Table of n, a(n) for n = 1..135

Example

a(5) = 120 because:
A140635(5) = 2 and LCM of 5 and 2 is 10,
A140635(10) = 6 and LCM of 10 and 6 is 30,
A140635(30) = 24 and LCM of 30 and 24 is 120,
A140635(120) = 120 so a(5) = 120.
From Hartmut F. W. Hoft, Mar 14 2023: (Start)
Table of iteration steps starting at n and ending with fixed point a(n):
    1  ...
    2  ...
    3    6   ...
    4  ...
    5   10    30   120    ...
    6    6   ...
    7   14    42   168    840     ...
    8   24   ...
    9   36   ...
   10   30   120   ...
   11   22    66   264   1320    9240   83160       ...
   12  ...
   13   26    78   312   1560   10920   98280   1081080  ...
   14   42   168   840    ...
   15   30   120   ...
   16  ...
  ... (End)

Mathematica

(* a005179[ ] based on the function by Vaclav Kotesovec in A005179 *)
mp[1, m_] := {{}}; mp[n_, 1] := {{}}; mp[n_?PrimeQ, m_] := If[m<n, {}, {{n}}];
mp[n_, m_] := Join@@Table[Map[Prepend[#, d]&, mp[n/d, d]], {d, Select[Rest[Divisors[n]], #<=m&]}]; mp[n_] := mp[n, n];
a005179[n_] := Module[{mulpar}, mulpar=mp[n]-1; Min[Table[Product[Prime[s]^mulpar[[j, s]], {s, 1, Length[mulpar[[j]]]}], {j, 1, Length[mulpar]}]]]
a306585[n_] := FixedPoint[LCM[#, a005179[DivisorSigma[0, #]]]&, n]
Map[a306585, Range[37]]  (* Hartmut F. W. Hoft, Mar 14 2023 *)

Prog

(PARI)
s(n) = my(nd=numdiv(n)); for(k=1, n, if(numdiv(k) == nd, return(k))); \\ A140635
a(n) = my(m=n, t=s(n)); while(1, m=lcm(m, t); t=s(m); if(m==t, return(m))); \\ Daniel Suteu, Feb 25 2019

Crossrefs

Cf. A005179, A007416, A140635.

Sequence in context: A072513 A022404 A210420 * A118138 A240023 A004583

Adjacent sequences: A306582 A306583 A306584 * A306586 A306587 A306588

Keyword

nonn

Author

J. Lowell, Feb 25 2019

Extensions

a(13)-a(37) from Rémy Sigrist, Feb 25 2019

Terms a(38) and beyond from Hartmut F. W. Hoft, Mar 14 2023

Status

approved