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A320629
Products of odd primes of nonprime index.
17
1, 7, 13, 19, 23, 29, 37, 43, 47, 49, 53, 61, 71, 73, 79, 89, 91, 97, 101, 103, 107, 113, 131, 133, 137, 139, 149, 151, 161, 163, 167, 169, 173, 181, 193, 197, 199, 203, 223, 227, 229, 233, 239, 247, 251, 257, 259, 263, 269, 271, 281, 293, 299, 301, 307, 311
OFFSET
1,2
COMMENTS
The index of a prime number n is the number m such that n is the m-th prime.
The asymptotic density of this sequence is (1/2) * Product_{p in A006450} (1 - 1/p) = 1/(2*Sum_{n>=1} 1/A076610(n)) < 1/6. - Amiram Eldar, Feb 02 2021
LINKS
EXAMPLE
The sequence of terms begins:
1 = 1
7 = prime(4)
13 = prime(6)
19 = prime(8)
23 = prime(9)
29 = prime(10)
37 = prime(12)
43 = prime(14)
47 = prime(15)
49 = prime(4)^2
53 = prime(16)
61 = prime(18)
71 = prime(20)
73 = prime(21)
79 = prime(22)
89 = prime(24)
91 = prime(4)*prime(6)
97 = prime(25)
101 = prime(26)
103 = prime(27)
107 = prime(28)
113 = prime(30)
131 = prime(32)
133 = prime(4)*prime(8)
137 = prime(33)
139 = prime(34)
149 = prime(35)
151 = prime(36)
161 = prime(4)*prime(9)
MATHEMATICA
Select[Range[1, 100, 2], And@@Not/@PrimeQ/@PrimePi/@First/@FactorInteger[#]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 18 2018
STATUS
approved