A379773 Numbers that set records in in A379772.
24, 96, 384, 1080, 2160, 4320, 8640, 12960, 17280, 34560, 38880, 69120, 77760, 108000, 155520, 311040, 432000, 622080, 756000, 1512000, 2268000, 3024000, 4536000, 5292000, 6804000, 9072000, 12096000, 13608000, 21168000, 27216000, 47628000, 54432000, 74088000, 81648000
Offset: 1
Keywords
Examples
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
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.
Programs
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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]]
Comments