OFFSET
1,1
COMMENTS
Product of 15 not necessarily distinct primes.
Divisible by exactly 15 prime powers (not including 1).
Any 15-almost prime can be represented in several ways as a product of three 5-almost primes A014614, and in several ways as a product of five 3-almost primes A014612. - Jonathan Vos Post, Dec 11 2004
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 = 15.
MATHEMATICA
Select[Range[90000], Plus @@ Last /@ FactorInteger[ # ] == 15 &] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2008 *)
Select[Range[450000], PrimeOmega[#]==15&] (* Harvey P. Dale, Aug 14 2019 *)
PROG
(PARI) k=15; start=2^k; finish=500000; 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), A069274 (r = 13), A069275 (r = 14), this sequence (r = 15), A069277 (r = 16), A069278 (r = 17), A069279 (r = 18), A069280 (r = 19), A069281 (r = 20). - Jason Kimberley, Oct 02 2011
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Mar 13 2002
STATUS
approved