A106349 Primes indexed by semiprimes.

7, 13, 23, 29, 43, 47, 73, 79, 97, 101, 137, 139, 149, 163, 167, 199, 227, 233, 257, 269, 271, 293, 313, 347, 373, 389, 421, 439, 443, 449, 467, 487, 491, 499, 577, 607, 631, 647, 653, 661, 673, 677, 727, 751, 757, 811, 821, 823, 829, 839, 907, 929, 937, 947

Offset

1,1

Comments

This is the sequence of the n-th prime for n = {4,6,9,10,14,15,21,22,25,26,33,34,35,38,39,46,49,51,...}. Not to be confused with A106350: semiprimes indexed by primes.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = prime(semiprime(n)).

a(n) = A000040(A001358(n)).

pi(a(n)) = p*q for some primes p and q.

Example

a(1) = 7 because semiprime(1) = 4, so prime(semiprime(1)) = prime(4) = 7.

Mathematica

Prime@ Select[Range@ 161, PrimeOmega@ # == 2 &] (* or *) Select[Prime@ Range@ 161, PrimeOmega@ PrimePi@ # == 2 &] (* Michael De Vlieger, Nov 28 2015 *)

Prog

(Magma) [NthPrime(n): n in [2..200] | &+[d[2]: d in Factorization(n)] eq 2]; // Vincenzo Librandi, Nov 28 2015
(PARI) lista(nn) = select(x->(bigomega(primepi(x))==2), primes(nn)); \\ Michel Marcus, Nov 29 2015

Crossrefs

Cf. A000040, A001358, A007097, A091022, A105997, A105998, A106350.

Sequence in context: A043104 A339112 A340020 * A293657 A048449 A147812

Adjacent sequences: A106346 A106347 A106348 * A106350 A106351 A106352

Keyword

nonn,easy

Author

Jonathan Vos Post, Apr 29 2005

Status

approved