A385417 Numbers with a record number of unordered factorizations into exponentially odd numbers (A268335).
1, 6, 24, 30, 60, 96, 120, 210, 240, 420, 480, 720, 840, 1680, 2520, 3360, 5040, 6720, 9240, 10080, 13440, 15120, 18480, 27720, 30240, 36960, 55440, 73920, 110880, 147840, 166320, 221760, 332640, 443520, 665280, 720720, 887040, 960960, 1108800, 1330560, 1441440
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..86
- Amiram Eldar, Table of n, a(n), A385416(a(n)) for n = 1..86.
Programs
-
Mathematica
T[n_, k_] := T[n, k] = If[n == 1 || k == 1, {{}}, Flatten[Table[Map[Prepend[#, d] &, T[d, k/d]], {d, Select[Divisors[k], 1 < # <= n &]}], 1]]; f[n_] := T[n, n]; expOdd[n_] := AllTrue[FactorInteger[n][[;; , 2]], OddQ]; s[n_] := Count[f[n], _?(And @@ (expOdd /@ #) &)]; With[{lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {, }][[;; , 2]]}, sm = -1; seq = {}; Do[s1 = s[lps[[i]]]; If[s1 > sm, sm = s1; AppendTo[seq, lps[[i]]]], {i, 1, 300}]; seq]
Formula
The factorizations of the first 5 terms:
n | a(n) | A385416(a(n)) | factorizations
--+-------+---------------|------------------------------------------------------------------
1 | 1 | 1 | 1
2 | 6 | 2 | 2*3, 6
3 | 24 | 4 | 2 * 2 * 2 * 3, 2 * 2 * 6, 3 * 8, 24
4 | 30 | 5 | 2 * 3 * 5, 2 * 15, 3 * 10, 5 * 6, 30
5 | 60 | 6 | 2 * 2 * 3 * 5, 2 * 2 * 15, 2 * 3 * 10, 2 * 5 * 6, 2 * 30, 6 * 10
Comments