cp's OEIS Frontend

A320629 Products of odd primes of nonprime index.

%I A320629 #10 Feb 02 2021 04:35:03
%S A320629 1,7,13,19,23,29,37,43,47,49,53,61,71,73,79,89,91,97,101,103,107,113,
%T A320629 131,133,137,139,149,151,161,163,167,169,173,181,193,197,199,203,223,
%U A320629 227,229,233,239,247,251,257,259,263,269,271,281,293,299,301,307,311
%N A320629 Products of odd primes of nonprime index.
%C A320629 The index of a prime number n is the number m such that n is the m-th prime.
%C A320629 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 A320629 Amiram Eldar, <a href="/A320629/b320629.txt">Table of n, a(n) for n = 1..10000</a>
%e A320629 The sequence of terms begins:
%e A320629     1 = 1
%e A320629     7 = prime(4)
%e A320629    13 = prime(6)
%e A320629    19 = prime(8)
%e A320629    23 = prime(9)
%e A320629    29 = prime(10)
%e A320629    37 = prime(12)
%e A320629    43 = prime(14)
%e A320629    47 = prime(15)
%e A320629    49 = prime(4)^2
%e A320629    53 = prime(16)
%e A320629    61 = prime(18)
%e A320629    71 = prime(20)
%e A320629    73 = prime(21)
%e A320629    79 = prime(22)
%e A320629    89 = prime(24)
%e A320629    91 = prime(4)*prime(6)
%e A320629    97 = prime(25)
%e A320629   101 = prime(26)
%e A320629   103 = prime(27)
%e A320629   107 = prime(28)
%e A320629   113 = prime(30)
%e A320629   131 = prime(32)
%e A320629   133 = prime(4)*prime(8)
%e A320629   137 = prime(33)
%e A320629   139 = prime(34)
%e A320629   149 = prime(35)
%e A320629   151 = prime(36)
%e A320629   161 = prime(4)*prime(9)
%t A320629 Select[Range[1,100,2],And@@Not/@PrimeQ/@PrimePi/@First/@FactorInteger[#]&]
%Y A320629 Cf. A000040, A006450, A007821, A018252, A056239, A076610, A112798, A302242, A320533, A320628, A320630, A320631, A320633.
%K A320629 nonn
%O A320629 1,2
%A A320629 _Gus Wiseman_, Oct 18 2018