OFFSET
1,1
COMMENTS
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..171
Michael De Vlieger, Prime power decomposition of a(n), n = 1..171.
Michael De Vlieger, List of (d, k/d), d < k/d, k = a(n), n = 1..24, such that gcd(d, k/d) > 1, and shown in blue, rad(d) | k/d though d does not divide k/d, but rad(k/d) does not divide d, while in gold, rad(d) does not divide k/d but rad(k/d) | d though k/d does not divide d.
EXAMPLE
Let b(n) = A379772(n).
Table showing exponents of prime power factors of a(n) for n = 1..20.
Example: a(5) = 2160 = 2^4 * 3^3 * 5, hence we write "4.3.1".
n a(n) Exp. b(a(n))
----------------------------------
1 24 3.1 1 4*6
2 96 5.1 2 6*16 = 8*12
3 384 7.1 3 6*64 = 12*32 = 16*24
4 1080 3.3.1 5 4*270 = 9*120 = 12*90 = 18*60 = 30*36
5 2160 4.3.1 6 8*270 = 9*240 = 18*120 = 24*90 = 30*72 = 36*60
6 4320 5.3.1 9
7 8640 6.3.1 10
8 12960 5.4.1 11
9 17280 7.3.1 13
10 34560 8.3.1 14
11 38880 5.5.1 16
12 69120 9.3.1 17
MATHEMATICA
(* Load function f at A025487 *)
r = 0; s = Select[Union@ Flatten@ f[8][[3 ;; -1]], Not @* SquareFreeQ];
rad[x_] := Times @@ FactorInteger[x][[All, 1]]; nn = Length[s];
Reap[Do[k = s[[i]];
If[# > r, r = #; Sow[k] ] &@
Count[Transpose@ {#, k/#} &@ #[[2 ;; Ceiling[Length[#]/2]]] &@ Divisors[k],
_?(m = GCD @@ {##};
And[! MemberQ[{1, #1, #2}, m],
And[PrimeNu[#1] < PrimeNu[#2], Divisible[#2, rad[#1]]] & @@
SortBy[{##}, PrimeNu]]) & @@ # &)], {i, nn}] ][[-1, 1]] ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Jan 04 2025
STATUS
approved