%I #36 Jun 14 2022 08:51:05

%S 1,3,15,105,1155,1365,19635,23205,636405,10555545,24484845,869107785,

%T 14797252681546335,92442344345566215,40334203530676690635,

%U 1451417351374223318085,6087255082617244520985,469256253416014832182075245585,1519012498286389398934397206158552189345

%N Records in A076978, divided by 2.

%H Hugo Pfoertner, <a href="/A354218/b354218.txt">Table of n, a(n) for n = 1..52</a>.

%t 1/2*Union@ FoldList[Max, Array[Times @@ FactorInteger[Times @@ Range[#1 + 1, #2 - 1]][[All, 1]] & @@ Map[Prime, # + {0, 1}] &, 180, 2]] (* _Michael De Vlieger_, May 20 2022 *)

%o (Python)

%o from sympy import sieve as p, primefactors

%o def A076978_halfen(n): # for all integers n > 1

%o result = 1

%o for composites in range(p[n]+1, p[n+1]):

%o for primefactor in primefactors(composites):

%o if result % primefactor != 0: result *= primefactor

%o return result//2

%o A354218 = [1]

%o for n in range(2,180):

%o if A076978_halfen(n) > A354218[-1]: A354218.append(A076978_halfen(n))

%o print(A354218) # _Karl-Heinz Hofmann_, May 20 2022

%o (PARI) a354218(maxterm) = {my(mp=0,pp=3); forprime(p=5,oo, my(L=List());for(j=pp+1,p-1, my(f=factor(j), nf=#f~); for(k=1,nf, listput(~L,f~[1,k]))); listsort(L,1); my(mpp=prod(k=1,#L,L[k])); if(mpp>mp, if(mpp<2*maxterm, print1(mpp/2,", "); mp=mpp, return)); pp=p)};

%o a354218(10^75)

%Y Cf. A007947, A076978, A354217.

%K nonn

%O 1,2

%A _Hugo Pfoertner_, May 19 2022