cp's OEIS Frontend

A267422 Largest prime factor of the largest squarefree practical number comprising n prime factors.

%I A267422 #24 Aug 08 2025 14:20:47
%S A267422 2,3,13,167,28219,796481281,634382430983400959,
%T A267422 402441068740409482305343048128921493,
%U A267422 161958813808922990180784918278423278413890512706478208244331277280870341
%N A267422 Largest prime factor of the largest squarefree practical number comprising n prime factors.
%C A267422 The prime factors of the largest squarefree practical number with n prime factors are the first n members of a(n). The largest squarefree practical number with 3 prime factors is 78 = 2*3*13 and the largest squarefree practical number with 5 prime factors is 367580694 = 2*3*13*167*28219, etc.
%C A267422 Because all primorial numbers (A002110) are practical, the prime factors of the smallest squarefree practical number with n prime factors are the first n members of the primes. Hence the smallest squarefree practical number with n prime factors is A002110(n). - _Frank M Jackson_, May 29 2023
%H A267422 Frank M Jackson, <a href="/A267422/b267422.txt">Table of n, a(n) for n = 1..15</a>
%H A267422 Wikipedia, <a href="http://en.wikipedia.org/wiki/Practical_number">Practical number</a> and <a href="http://en.wikipedia.org/wiki/Squarefree_integer">Squarefree integer</a>
%e A267422 a(3) = 13 because there are only 4 squarefree practical numbers with 3 prime factors, namely 2*3*5 = 30, 2*3*7 = 42, 2*3*11 = 66 and 2*3*13 = 78. So 78 is the largest squarefree practical number with 3 prime factors and the largest prime factor is 13.
%t A267422 lst={2}; Do[If[PrimeQ[f=DivisorSigma[1, Apply[Times, lst]]+1], AppendTo[lst, f], AppendTo[lst, NextPrime[f, -1]]], {8}]; lst
%t A267422 lst={2}; Do[AppendTo[lst, NextPrime[Times@@(#+1)&[lst]+2, -1]], {12}]; lst (* _Frank M Jackson_, May 29 2023 *)
%Y A267422 Cf. A002110, A005117, A005153, A265501.
%K A267422 nonn
%O A267422 1,1
%A A267422 _Frank M Jackson_, Jan 14 2016