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 A328520 #21 Jan 14 2020 01:40:19
%S A328520 1,2,2,12,12,12,60,120,2520,2520,2520,55440,55440,720720,720720,
%T A328520 12252240,36756720,698377680,3491888400,80313433200,160626866400,
%U A328520 160626866400,9316358251200,288807105787200,2021649740510400,74801040398884800,74801040398884800,3066842656354276800,131874234223233902400
%N A328520 GCD of terms in A002182 that have n prime factors counted with multiplicity.
%C A328520 If for every term t > 1 in A002182 there exists a term in A002182 of the form t/p for some prime p|t (Cf. A328523) then (1): a(n+1) is a multiple of a(n) for n >= 1 and (2): this sequence can be used to find terms to A199337 and A330737.
%C A328520 Proof of (1): Let Generation(n) be the terms in A002182 with n prime factors counted with multiplicity. Then a(n) = GCD(Generation(n)). As each term in Generation(n) is of the form a(n) * t for some t and each term in Generation(n + 1) is p * g for some g in Generation(n), a(n + 1) is a multiple of a(n).
%C A328520 Proof of (2): As a(n + 1) is a multiple of a(n) we have that if m | a(n), we also have m | a(n + k), k >= 0 hence the largest number not divisible by m can have at most n - 1 prime factors counted with multiplicity.
%C A328520 Given Generation(n) we can find all candidates for Generation(n + 1) and from there on find terms to A002182, A199337 and A330737.
%e A328520 The terms in A002182 with n = 4 prime divisors counted with multiplicity are 24, 36 and 60. Their GCD is 12 hence a(4) = 12.
%e A328520 Furthermore, If for every term t > 1 in A002182 there exists a term in A002182 of the form t/p for some prime p|t then we have that each term with more than 4 prime divisors counted with multiplicity is a multiple of at least one of 24, 36 or 60 hence is divisible by 12.
%t A328520 (* First, load the function f at A025487, then: *)
%t A328520 Block[{s = Union@ Flatten@ f@ 20, t}, t = DivisorSigma[0, s]; s = Map[s[[FirstPosition[t, #][[1]] ]] &, Union@ FoldList[Max, t]]; t = PrimeOmega[s]; Drop[Array[GCD @@ s[[Position[t, #][[All, 1]] ]] &, Max@ t + 1, 0], -3] ] (* _Michael De Vlieger_, Jan 12 2020 *)
%Y A328520 Cf. A001222, A002182, A199337, A328523, A330737
%Y A328520 Cf. also A054481.
%K A328520 nonn
%O A328520 0,2
%A A328520 _David A. Corneth_, Jan 04 2020