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
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