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 A305398 Index of the least prime not dividing p-1, where p = A073918(n) is the smallest prime such that p-1 has n distinct prime factors. 1
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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 EXAMPLE 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 + 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

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Last modified May 31 22:11 EDT 2020. Contains 334756 sequences. (Running on oeis4.)