

A305399


Index of the largest prime dividing p1, where p = A073918(n) is the smallest prime such that p1 has n distinct prime factors; a(0) = 0.


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


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.


LINKS

Table of n, a(n) for n=0..82.


EXAMPLE

For 0 <= n <= 5, the smallest prime p = A073918(n) such that p1 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.


PROG

(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.


CROSSREFS

Cf. A073918, A002110.
Sequence in context: A085266 A280431 A056804 * A101547 A047597 A309960
Adjacent sequences: A305396 A305397 A305398 * A305400 A305401 A305402


KEYWORD

nonn


AUTHOR

M. F. Hasler, May 31 2018


STATUS

approved



