A069274 13-almost primes (generalization of semiprimes).

8192, 12288, 18432, 20480, 27648, 28672, 30720, 41472, 43008, 45056, 46080, 51200, 53248, 62208, 64512, 67584, 69120, 69632, 71680, 76800, 77824, 79872, 93312, 94208, 96768, 100352, 101376, 103680, 104448, 107520, 112640, 115200

Offset

1,1

Comments

Product of 13 not necessarily distinct primes.

Divisible by exactly 13 prime powers (not including 1).

Links

D. W. Wilson, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Almost Prime.

Formula

Product p_i^e_i with Sum e_i = 13.

Mathematica

Select[Range[30000], Plus @@ Last /@ FactorInteger[ # ] == 13 &] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2008 *)
Select[Range[116000], PrimeOmega[#]==13&] (* Harvey P. Dale, Mar 11 2019 *)

Prog

(PARI) k=13; start=2^k; finish=130000; v=[] for(n=start, finish, if(bigomega(n)==k, v=concat(v, n))); v

Crossrefs

Sequences listing r-almost primes, that is, the n such that A001222(n) = r: A000040 (r = 1), A001358 (r = 2), A014612 (r = 3), A014613 (r = 4), A014614 (r = 5), A046306 (r = 6), A046308 (r = 7), A046310 (r = 8), A046312 (r = 9), A046314 (r = 10), A069272 (r = 11), A069273 (r = 12), this sequence (r = 13), A069275 (r = 14), A069276 (r = 15), A069277 (r = 16), A069278 (r = 17), A069279 (r = 18), A069280 (r = 19), A069281 (r = 20). - Jason Kimberley, Oct 02 2011

Sequence in context: A289477 A222527 A035908 * A220585 A305756 A195661

Adjacent sequences: A069271 A069272 A069273 * A069275 A069276 A069277

Keyword

nonn

Author

Rick L. Shepherd, Mar 13 2002

Status

approved