A354217 - OEIS

%I #10 May 20 2022 09:26:34

%S 3,5,7,13,19,23,31,47,53,73,83,89,113,199,211,293,467,523,887,1129,

%T 1327,2971,3271,4297,4831,5591,8467,9551,12853,14107,15683,19609,

%U 25471,31397,89689,107377,134513,155921,265621,338033,360653,370261,492113,1098847,1349533

%N 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.

%t 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 *)

%o (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)};

%o a354217(1500000)

%Y Cf. A007947, A076978, A354218.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, May 19 2022