A124268 Primes indexed by 3-almost primes.

19, 37, 61, 71, 103, 107, 113, 181, 193, 197, 229, 239, 307, 317, 337, 349, 379, 383, 397, 479, 521, 523, 557, 571, 601, 619, 641, 643, 683, 691, 733, 787, 853, 857, 883, 887, 971, 977, 1013, 1019, 1021, 1033, 1039, 1091, 1109, 1123, 1151, 1187, 1279

Offset

1,1

Comments

3-almost primes indexed by primes = A124269. prime(3almostprime(n)) - 3almostprime(prime(n)) = A124270. See also A106349 Primes indexed by semiprimes. See also A106350 Semiprimes indexed by primes. See also A122824 Prime(semiprime(n)) - semiprime(prime(n)). Commutator [A000040,A001358] at n.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Formula

a(n) = prime(3almostprime(n)) = A000040(A014612(n)). {p such that p is prime and omega(primepi(p)) = 3} = {p such that p is in A000040 and A001222(A000720(p)) = 3}.

Example

a(1) = prime(3almostprime(1)) = prime(8) = 19.
a(2) = prime(3almostprime(2)) = prime(12) = 37.
a(3) = prime(3almostprime(3)) = prime(18) = 61.

Mathematica

Prime[#]&/@Select[Range[400], PrimeOmega[#]==3&] (* Harvey P. Dale, Mar 19 2020 *)

Crossrefs

Cf. A000040, A014612, A122824, A124269, A124270.

Sequence in context: A131600 A175546 A162471 * A339860 A259648 A154944

Adjacent sequences: A124265 A124266 A124267 * A124269 A124270 A124271

Keyword

easy,nonn

Author

Jonathan Vos Post, Oct 23 2006

Status

approved