cp's OEIS Frontend

A305399 Index of the largest prime dividing p-1, where p = A073918(n) is the smallest prime such that p-1 has n distinct prime factors; a(0) = 0.

%I A305399 #4 Jun 01 2018 08:07:47
%S A305399 0,1,2,3,4,5,8,10,9,11,11,11,14,15,17,16,18,21,21,24,23,22,23,27,30,
%T A305399 26,29,31,29,30,35,34,39,36,39,37,39,41,39,43,42,43,46,45,45,46,51,52,
%U A305399 49,53,56,58,58,54,58,56,59,61,60,62,63,66,66,65,65,68,68,71,70,71,73,72,73,75,75,75,78,79,82,83,89,83,85
%N A305399 Index of the largest prime dividing p-1, where p = A073918(n) is the smallest prime such that p-1 has n distinct prime factors; a(0) = 0.
%C A305399 For 0 <= n <= 5, A073918(n) = A002110(n) + 1 = prime(n)# + 1, therefore a(n) = n. From n >= 6 on, some smaller primes are missing in the factorization of A073918(n) - 1, whence a(n) > n.
%C A305399 This is related to the question whether lim sup A073918(n)/A002110(n) has a finite value.
%e A305399 For 0 <= n <= 5, the smallest prime p = A073918(n) such that p-1 has n distinct prime factors is p = prime(n)# + 1, therefore a(n) = n is the index of the largest prime dividing p - 1.
%e A305399 For n = 6, the smallest prime p such that p - 1 has 6 distinct prime factors is prime(5)#*prime(8) + 1, therefore a(n) = 8.
%o A305399 (PARI) a(n)=if(n,primepi(vecmax(factor(A073918(n)-1)[,1]))) \\ For illustration; it is more efficient to adapt code from A073918 to compute the sequence.
%Y A305399 Cf. A073918, A002110.
%K A305399 nonn
%O A305399 0,3
%A A305399 _M. F. Hasler_, May 31 2018