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.

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, 26, 29, 31, 29, 30, 35, 34, 39, 36, 39, 37, 39, 41, 39, 43, 42, 43, 46, 45, 45, 46, 51, 52, 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

Offset: 0

Author

M. F. Hasler, May 31 2018

Keywords

• nonn

Comments

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.

This is related to the question whether lim sup A073918(n)/A002110(n) has a finite value.

Examples

			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.
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.
		

Crossrefs

Cf. A073918, A002110.

Programs

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.