A124309 5-almost primes indexed by primes.

48, 72, 108, 120, 180, 208, 270, 280, 368, 420, 450, 520, 592, 612, 660, 700, 760, 828, 920, 952, 976, 1032, 1064, 1128, 1242, 1288, 1323, 1372, 1380, 1428, 1575, 1624, 1674, 1700, 1752, 1768, 1880, 1976, 2028, 2096, 2178, 2196, 2312, 2328, 2384, 2394, 2475

Offset: 1

Author

Jonathan Vos Post, Oct 25 2006

Keywords

• easy
• nonn
• less

Examples

			a(1) = 5almostprime(prime(1)) = 5almostprime(2) = 48 = 2^4 * 3.
a(2) = 5almostprime(prime(2)) = 5almostprime(3) = 72 = 2^3 * 3^2.
a(3) = 5almostprime(prime(3)) = 5almostprime(5) = 108 = 2^2 * 3^3.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A124308 Primes indexed by 5-almost 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, A124282-A124284, A124309.

Programs

PARI

list(lim)=my(v=List(),u=v); forprime(p=2,lim\16, forprime(q=2,min(lim\(8*p),p), forprime(r=2,min(lim\(4*p*q),q), forprime(s=2,min(lim\(2*p*q*r),r), forprime(t=2,min(lim\(p*q*r*s),s), listput(v,p*q*r*s*t)))))); v=Set(v); forprime(p=2,#v, listput(u,v[p])); v=0; Vec(u) \\ Charles R Greathouse IV, Feb 10 2017

Formula

a(n) = 5almostprime(prime(n)) = A014614(A000040(n)).

Extensions

a(16)-a(47) from Giovanni Resta, Jun 13 2016