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 A354219 #15 Jun 20 2025 20:22:23
%S A354219 3,5,7,13,19,31,53,73,89,113,211,293,523,887,1129,1327,4297,4831,5351,
%T A354219 5591,8467,12853,15683,19609,25471,31397,134513,155921,338033,360653,
%U A354219 370261,492113,1349533,1357201,1561919,2010733,4652353,8421251,11113933,15203977,17051707
%N A354219 Primes p such that the number of distinct prime factors omega of the product of the composite numbers between p and the next prime after p sets a new record.
%e A354219 a(6) = 31, because the first product of consecutive composites with 6 primes in its squarefree kernel is P = 32*33*34*35*36 with rad(P) = 2*3*5*7*11*17 = 39270, whereas the interval starting after A354217(6) = 23 leads only to 5 distinct factors, i.e., rad(24*25*26*27*28) = 2*3*5*7*13, not sufficient to beat the record set by the composites after a(5) = A354217(5) = 19 with rad(20*21*22) = 2*3*5*7*11.
%t A354219 s = Array[PrimeNu[Times @@ FactorInteger[Times @@ Range[#1 + 1, #2 - 1]][[All, 1]] & @@ Map[Prime, # + {0, 1}]] &, 10^4]; Prime@ Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]] (* _Michael De Vlieger_, May 20 2022 *)
%t A354219 DeleteDuplicates[Table[{p,Length[Union[Flatten[FactorInteger[#][[;;,1]]&/@Range[p+1,NextPrime[p]-1]]]]},{p,Prime[Range[ 2,10^6]]}], GreaterEqual[ #1[[2]],#2[[2]]]&][[;;,1]] (* The program generates the first 40 terms of the sequence, i.e., every term up to the 1 millionth prime. *) (* _Harvey P. Dale_, Feb 01 2025 *)
%Y A354219 A354220 provides the corresponding values of omega.
%Y A354219 Cf. A001221, A076978, A354217.
%K A354219 nonn
%O A354219 1,1
%A A354219 _Hugo Pfoertner_, May 20 2022