A354218 Records in A076978, divided by 2.

1, 3, 15, 105, 1155, 1365, 19635, 23205, 636405, 10555545, 24484845, 869107785, 14797252681546335, 92442344345566215, 40334203530676690635, 1451417351374223318085, 6087255082617244520985, 469256253416014832182075245585, 1519012498286389398934397206158552189345

Offset: 1

Author

Hugo Pfoertner, May 19 2022

Keywords

• nonn

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..52.

Crossrefs

Cf. A007947, A076978, A354217.

Programs

Mathematica

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 *)

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)};
a354218(10^75)

Python

from sympy import sieve as p, primefactors
def A076978_halfen(n): # for all integers n > 1
    result = 1
    for composites in range(p[n]+1, p[n+1]):
        for primefactor in primefactors(composites):
            if result % primefactor != 0: result *= primefactor
    return result//2
A354218 = [1]
for n in range(2,180):
    if  A076978_halfen(n) > A354218[-1]: A354218.append(A076978_halfen(n))
print(A354218) # Karl-Heinz Hofmann, May 20 2022