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 A283990 #12 Mar 23 2017 11:44:46
%S A283990 1,2,2,8,2,144,2,64,8,1152,2,124416,2,1152,144,1024,2,35831808,2,
%T A283990 221184,144,18432,2,859963392,8,18432,64,221184,2,261213880320000000,
%U A283990 2,32768,1152,589824,144,26748301344768,2,589824,1152,1528823808,2,12036735605145600000,2,7077888,124416,589824,2,1283918464548864,8,27518828544,1152,7077888,2,69331597085638656,144
%N A283990 a(n) = A046523(A243103(n)).
%C A283990 Irregular triangle A162306(n) lists numbers 1 <= m <= n with m | n^e and e >= 0 of which A243103(n) is the product. The numbers m in this range have prime factors p that also divide n, with 1 the empty product that divides n; a(1) = 1 because 1 is the empty product and has no prime factors.
%C A283990 For prime p, a(p) = 2 since A162306(p) = {1,p}, the product of which is p. The smallest number with prime signature of a prime is the smallest prime, 2.
%C A283990 For prime power n = p^e, a(p^e) = 2^A000217(e), since A162306(p^e) is the power range 0..e of p | n.
%C A283990 The sequence can also be produced by raising the multiplicities m listed in A283866(n) = T(n,k) to the prime corresponding to their order in row n, i.e., prime(k)^m, and taking the product.
%H A283990 Antti Karttunen (terms 1..255) and Michael De Vlieger, <a href="/A283990/b283990.txt">Table of n, a(n) for n = 1..4619</a>
%F A283990 a(n) = A046523(A243103(n)).
%e A283990 a(9) = 8 since A162306(9) = {1,3,9}, the product of which is 27 = 3^3; 2 is the smallest prime, thus a(9) = 2^3 = 8.
%e A283990 a(15) = 144 since A162306(15) = {1,3,5,9,15}, the product of which is 2025 = 3^4 * 5^2; applying these multiplicities to the smallest primes in their order gives us 2^4 * 3^2 = 144.
%e A283990 a(4620) = 2^908 * 3^511 * 5^299 * 7^220 * 11^155 has 1072 decimal digits.
%t A283990 Table[If[n == 1, 1, Times @@ MapIndexed[Prime[First[#2]]^#1 &, FactorInteger[Apply[Times, Select[Range@ n, PowerMod[n, Floor@ Log2@ n, #] == 0 &]]][[All, -1]]]], {n, 55}] (* or *)
%t A283990 Table[Times @@ MapIndexed[Prime[First@ #2]^#1 &, With[{m = Floor@ Log2@ n}, Values@ Merge[Association /@ Map[#1 -> #2 & @@ # &, FactorInteger@ Rest@ Select[Range@ n, PowerMod[n, m, #] == 0 &], {2}], Total]] /. {} -> {0}], {n, 10^4}] (* _Michael De Vlieger_, Mar 22 2017, Version 10, faster *)
%o A283990 (Scheme) (define (A283990 n) (A046523 (A243103 n)))
%Y A283990 Cf. A046523, A162306, A243103, A283866, A283995.
%K A283990 nonn
%O A283990 1,2
%A A283990 _Antti Karttunen_ and _Michael De Vlieger_, Mar 22 2017