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

Author

Jonathan Vos Post, Oct 23 2006

Keywords

• easy
• nonn

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.

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

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}.