A124308 Primes indexed by 5-almost primes.

131, 223, 359, 409, 593, 613, 659, 953, 997, 1049, 1069, 1223, 1283, 1543, 1601, 1693, 1733, 1747, 1811, 1987, 2003, 2069, 2503, 2593, 2693, 2713, 2789, 2801, 2903, 3079, 3181, 3221, 3301, 3323, 3541, 3571, 3727, 4003, 4127, 4283

Offset: 1

Author

Jonathan Vos Post, Oct 25 2006

Keywords

• easy
• nonn
• less

Examples

			a(1) = prime(5almostprime(1)) = prime(32 = 2^5) = 131.
a(2) = prime(5almostprime(2)) = prime(48 = 2^4 * 3) = 223.
a(3) = prime(5almostprime(3)) = prime(72 = 2^3 * 3^2) = 359.
a(4) = prime(5almostprime(4)) = prime(80 = 2^4 * 5) = 409.
		

Crossrefs

Cf. A124309 5-almost primes indexed by primes. A124310 prime(5almostprime(n)) - 5almostprime(prime(n)). 4-almost primes indexed by primes = A124283. prime(4almostprime(n)) - 4almostprime(prime(n)) = A124284. Primes indexed by 3-almost primes = A124268. 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.

Cf. A000040, A014614, A114405, A114415, A122824, A124269, A124270, A124282-A124284, A124309, A124310.

Programs

Mathematica

Prime[#]&/@Select[Range[600],PrimeOmega[#]==5&] (* Harvey P. Dale, Nov 20 2015 *)

Formula

a(n) = prime(5almostprime(n)) = A000040(A014614(n)). {p such that p is prime and omega(primepi(p)) = 5} = {p such that p is in A000040 and A001222(A000720(p)) = 5}.