A320629 Products of odd primes of nonprime index.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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[#]&]

Crossrefs

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

Sequence in context: A124095 A109369 A336373 * A371166 A340105 A309649

Adjacent sequences: A320626 A320627 A320628 * A320630 A320631 A320632

Keyword

nonn

Author

Gus Wiseman, Oct 18 2018

Status

approved