|
%I #15 Feb 02 2021 04:34:51
%S 1,2,4,7,8,13,14,16,19,23,26,28,29,32,37,38,43,46,47,49,52,53,56,58,
%T 61,64,71,73,74,76,79,86,89,91,92,94,97,98,101,103,104,106,107,112,
%U 113,116,122,128,131,133,137,139,142,146,148,149,151,152,158,161,163
%N Products of 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 Product_{p in A006450} (1 - 1/p) = 1/(Sum_{n>=1} 1/A076610(n)) < 1/3. - _Amiram Eldar_, Feb 02 2021
%H Amiram Eldar, <a href="/A320628/b320628.txt">Table of n, a(n) for n = 1..10000</a>
%e The sequence of terms begins:
%e 1 = 1
%e 2 = prime(1)
%e 4 = prime(1)^2
%e 7 = prime(4)
%e 8 = prime(1)^3
%e 13 = prime(6)
%e 14 = prime(1)*prime(4)
%e 16 = prime(1)^4
%e 19 = prime(8)
%e 23 = prime(9)
%e 26 = prime(1)*prime(6)
%e 28 = prime(1)^2*prime(4)
%e 29 = prime(10)
%e 32 = prime(1)^5
%e 37 = prime(12)
%e 38 = prime(1)*prime(8)
%e 43 = prime(14)
%e 46 = prime(1)*prime(9)
%e 47 = prime(15)
%e 49 = prime(4)^2
%e 52 = prime(1)^2*prime(6)
%e 53 = prime(16)
%e 56 = prime(1)^3*prime(4)
%e 58 = prime(1)*prime(10)
%e 61 = prime(18)
%e 64 = prime(1)^6
%e 71 = prime(20)
%e 73 = prime(21)
%e 74 = prime(1)*prime(12)
%e 76 = prime(1)^2*prime(8)
%e 79 = prime(22)
%e 86 = prime(1)*prime(14)
%e 89 = prime(24)
%e 91 = prime(4)*prime(6)
%e 92 = prime(1)^2*prime(9)
%e 94 = prime(1)*prime(15)
%e 97 = prime(25)
%e 98 = prime(1)*prime(4)^2
%t Select[Range[100],And@@Not/@PrimeQ/@PrimePi/@First/@FactorInteger[#]&]
%Y Cf. A018252, A056239, A290103, A302242, A302478, A320533, A320629, A320630, A320631, A320633.
%Y Complement of A331386.
%Y Positions of zeros in A257994.
%Y Primes of prime index are A006450.
%Y Primes of nonprime index are A007821.
%Y Products of primes of prime index are A076610.
%Y Products of primes of nonprime index are this sequence.
%Y The number of prime prime indices is given by A257994.
%Y The number of nonprime prime indices is given by A330944.
%Y Cf. A000040, A000720, A001222, A112798, A295665.
%K nonn
%O 1,2
%A _Gus Wiseman_, Oct 18 2018
| 