

A069276


15almost primes (generalization of semiprimes).


28



32768, 49152, 73728, 81920, 110592, 114688, 122880, 165888, 172032, 180224, 184320, 204800, 212992, 248832, 258048, 270336, 276480, 278528, 286720, 307200, 311296, 319488, 373248, 376832, 387072, 401408, 405504, 414720, 417792, 430080
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Product of 15 not necessarily distinct primes.
Divisible by exactly 15 prime powers (not including 1).
Any 15almost prime can be represented in several ways as a product of three 5almost primes A014614, and in several ways as a product of five 3almost 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

Cf. A101637, A101638, A101605, A101606.
Sequences listing ralmost 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
Sequence in context: A222528 A232393 A217589 * A195235 A223335 A194934
Adjacent sequences: A069273 A069274 A069275 * A069277 A069278 A069279


KEYWORD

nonn


AUTHOR

Rick L. Shepherd, Mar 13 2002


STATUS

approved



