A124318 3-almost primes indexed by semiprimes.

20, 28, 44, 45, 66, 68, 98, 99, 110, 114, 147, 148, 153, 165, 170, 188, 207, 222, 238, 244, 245, 261, 273, 284, 310, 322, 343, 356, 357, 363, 374, 387, 388, 399, 429, 438, 465, 475, 477, 494, 498, 506, 531, 549, 555, 590, 595, 596, 602, 603, 628, 639, 642

Offset

1,1

Links

Table of n, a(n) for n=1..53.

Formula

a(n) = 3almostprime(semiprime(n)) = A014612(A001358(n)).

Example

a(1) = 3almostprime(semiprime(1)) = 3almostprime(4 = 2^2) = 20 = 2^2 * 5.
a(2) = 3almostprime(semiprime(2)) = 3almostprime(6 = 2 * 3) = 28 = 2^2 * 7.
a(3) = 3almostprime(semiprime(3)) = 3almostprime(9 = 3^2) = 44 = 2^2 * 11.
a(4) = 3almostprime(semiprime(4)) = 3almostprime(10 = 2 * 5) = 45 = 3^2 * 5.

Mathematica

p[k_] := Select[Range[1000], PrimeOmega[#] == k &]; p[3][[Take[p[2], 60]]] (* Giovanni Resta, Jun 13 2016 *)

Crossrefs

Cf. A124317 Semiprimes indexed by 3-almost primes. A124318 3-almost primes indexed by semiprimes. A124319 semiprime(3almostprime(n)) - 3almostprime(semiprime(n)). A124308 Primes indexed by 5-almost primes. 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, A001358, A014612, A065516, A114403, A122824, A124269, A124270, A124282-A124284, A124309, A124310, A124317, A124319.

Sequence in context: A361867 A309769 A252478 * A309780 A139703 A317924

Adjacent sequences: A124315 A124316 A124317 * A124319 A124320 A124321

Keyword

easy,nonn,less

Author

Jonathan Vos Post, Oct 26 2006

Extensions

a(22)-a(53) from Giovanni Resta, Jun 13 2016

Status

approved