This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379773 #9 Jul 12 2025 16:06:53
%S A379773 24,96,384,1080,2160,4320,8640,12960,17280,34560,38880,69120,77760,
%T A379773 108000,155520,311040,432000,622080,756000,1512000,2268000,3024000,
%U A379773 4536000,5292000,6804000,9072000,12096000,13608000,21168000,27216000,47628000,54432000,74088000,81648000
%N A379773 Numbers that set records in in A379772.
%C A379773 Proper subset of the intersection A025487 and A378767.
%C A379773 Conjecture: a(n) is powerful (i.e., in A286708) for n >= 68. Additionally, for some n much larger than 68, a(n) may be cubefull (i.e., in A372695).
%H A379773 Michael De Vlieger, <a href="/A379773/b379773.txt">Table of n, a(n) for n = 1..171</a>
%H A379773 Michael De Vlieger, <a href="/A379773/a379773.txt">Prime power decomposition of a(n)</a>, n = 1..171.
%H A379773 Michael De Vlieger, <a href="/A379773/a379773.png">List of (d, k/d), d < k/d, k = a(n)</a>, 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.
%e A379773 Let b(n) = A379772(n).
%e A379773 Table showing exponents of prime power factors of a(n) for n = 1..20.
%e A379773 Example: a(5) = 2160 = 2^4 * 3^3 * 5, hence we write "4.3.1".
%e A379773 n a(n) Exp. b(a(n))
%e A379773 ----------------------------------
%e A379773 1 24 3.1 1 4*6
%e A379773 2 96 5.1 2 6*16 = 8*12
%e A379773 3 384 7.1 3 6*64 = 12*32 = 16*24
%e A379773 4 1080 3.3.1 5 4*270 = 9*120 = 12*90 = 18*60 = 30*36
%e A379773 5 2160 4.3.1 6 8*270 = 9*240 = 18*120 = 24*90 = 30*72 = 36*60
%e A379773 6 4320 5.3.1 9
%e A379773 7 8640 6.3.1 10
%e A379773 8 12960 5.4.1 11
%e A379773 9 17280 7.3.1 13
%e A379773 10 34560 8.3.1 14
%e A379773 11 38880 5.5.1 16
%e A379773 12 69120 9.3.1 17
%t A379773 (* Load function f at A025487 *)
%t A379773 r = 0; s = Select[Union@ Flatten@ f[8][[3 ;; -1]], Not @* SquareFreeQ];
%t A379773 rad[x_] := Times @@ FactorInteger[x][[All, 1]]; nn = Length[s];
%t A379773 Reap[Do[k = s[[i]];
%t A379773 If[# > r, r = #; Sow[k] ] &@
%t A379773 Count[Transpose@ {#, k/#} &@ #[[2 ;; Ceiling[Length[#]/2]]] &@ Divisors[k],
%t A379773 _?((m = GCD @@ {##};
%t A379773 And[! MemberQ[{1, #1, #2}, m],
%t A379773 And[PrimeNu[#1] < PrimeNu[#2], Divisible[#2, rad[#1]]] & @@
%t A379773 SortBy[{##}, PrimeNu]]) & @@ # &)], {i, nn}] ][[-1, 1]]
%Y A379773 Cf. A025487, A378767, A379772, A379774.
%K A379773 nonn
%O A379773 1,1
%A A379773 _Michael De Vlieger_, Jan 04 2025