

A305398


Index of the least prime not dividing p1, where p = A073918(n) is the smallest prime such that p1 has n distinct prime factors.


1



1, 2, 3, 4, 5, 6, 6, 7, 7, 9, 10, 12, 11, 12, 13, 15, 16, 15, 16, 18, 19, 20, 21, 22, 22, 23, 25, 27, 26, 29, 29, 27, 31, 33, 32, 34, 36, 36, 38, 39, 35, 38, 40, 43, 38, 44, 46, 46, 45, 48, 50, 49, 49, 51, 50, 54, 54, 57, 58, 56, 57, 58, 58, 63, 62, 64, 63, 67, 64, 68, 69, 69, 70, 69, 74, 76, 71, 73, 76, 78, 80, 79, 80, 81, 84, 84, 83, 87, 88, 86, 88
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OFFSET

0,2


COMMENTS

For 0 <= n <= 5, A073918(n) = A002110(n) + 1 = prime(n)# + 1, therefore a(n) = n + 1. 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 conjecture formulated in A073918, that for any m there is K(m) such that prime(m)#  A073918(k)1 for all k >= K(m): This conjecture is equivalent to lim inf a(n) = oo.


LINKS

Table of n, a(n) for n=0..90.


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 + 1 is the index of the smallest prime not 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) = 6.


PROG

(PARI) a(n)={(n=factor(A073918(n)1)[, 1])&& for(i=2, #n, n[i]>prime(i)&&return(i)); #n+1} \\ For illustration; it is more efficient to adapt code from A073918 to compute the sequence.


CROSSREFS

Cf. A073918, A002110.
Sequence in context: A005376 A196362 A195879 * A216522 A086419 A287354
Adjacent sequences: A305395 A305396 A305397 * A305399 A305400 A305401


KEYWORD

nonn


AUTHOR

M. F. Hasler, May 31 2018


STATUS

approved



