A320629 - OEIS

%I #10 Feb 02 2021 04:35:03

%S 1,7,13,19,23,29,37,43,47,49,53,61,71,73,79,89,91,97,101,103,107,113,

%T 131,133,137,139,149,151,161,163,167,169,173,181,193,197,199,203,223,

%U 227,229,233,239,247,251,257,259,263,269,271,281,293,299,301,307,311

%N Products of odd primes of nonprime index.

%C The index of a prime number n is the number m such that n is the m-th prime.

%C 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

%H Amiram Eldar, <a href="/A320629/b320629.txt">Table of n, a(n) for n = 1..10000</a>

%e The sequence of terms begins:

%e     1 = 1

%e     7 = prime(4)

%e    13 = prime(6)

%e    19 = prime(8)

%e    23 = prime(9)

%e    29 = prime(10)

%e    37 = prime(12)

%e    43 = prime(14)

%e    47 = prime(15)

%e    49 = prime(4)^2

%e    53 = prime(16)

%e    61 = prime(18)

%e    71 = prime(20)

%e    73 = prime(21)

%e    79 = prime(22)

%e    89 = prime(24)

%e    91 = prime(4)*prime(6)

%e    97 = prime(25)

%e   101 = prime(26)

%e   103 = prime(27)

%e   107 = prime(28)

%e   113 = prime(30)

%e   131 = prime(32)

%e   133 = prime(4)*prime(8)

%e   137 = prime(33)

%e   139 = prime(34)

%e   149 = prime(35)

%e   151 = prime(36)

%e   161 = prime(4)*prime(9)

%t Select[Range[1,100,2],And@@Not/@PrimeQ/@PrimePi/@First/@FactorInteger[#]&]

%Y Cf. A000040, A006450, A007821, A018252, A056239, A076610, A112798, A302242, A320533, A320628, A320630, A320631, A320633.

%K nonn

%O 1,2

%A _Gus Wiseman_, Oct 18 2018