A354217 Primes p such that the squarefree kernel of the product of the composite numbers between p and the next prime after p (A076978) sets a new record.

3, 5, 7, 13, 19, 23, 31, 47, 53, 73, 83, 89, 113, 199, 211, 293, 467, 523, 887, 1129, 1327, 2971, 3271, 4297, 4831, 5591, 8467, 9551, 12853, 14107, 15683, 19609, 25471, 31397, 89689, 107377, 134513, 155921, 265621, 338033, 360653, 370261, 492113, 1098847, 1349533

Offset: 1

Author

Hugo Pfoertner, May 19 2022

Keywords

• nonn

Crossrefs

Cf. A007947, A076978, A354218.

Programs

Mathematica

s = Array[Times @@ FactorInteger[Times @@ Range[#1 + 1, #2 - 1]][[All, 1]] & @@ Map[Prime, # + {0, 1}] &, 2^15]; Prime@ Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]] (* Michael De Vlieger, May 20 2022 *)

PARI

a354217(limit) = {my(mp=0,pp=3); forprime(p=5,limit,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,print1(pp,", ");mp=mpp); pp=p)};
a354217(1500000)