

A046306


Numbers that are divisible by exactly 6 primes with multiplicity.


57



64, 96, 144, 160, 216, 224, 240, 324, 336, 352, 360, 400, 416, 486, 504, 528, 540, 544, 560, 600, 608, 624, 729, 736, 756, 784, 792, 810, 816, 840, 880, 900, 912, 928, 936, 992, 1000, 1040, 1104, 1134, 1176, 1184, 1188, 1215, 1224, 1232, 1260, 1312, 1320
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OFFSET

1,1


COMMENTS

Also called 6almost primes. Products of exactly 6 primes (not necessarily distinct). Any 6almost prime can be represented in several ways as a product of two 3almost primes A014612 and in several ways as a product of three semiprimes A001358.  Jonathan Vos Post, Dec 11 2004


LINKS

T. D. Noe, 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 = 6.
a(n) ~ 120n log n / (log log n)^5.  Charles R Greathouse IV, May 06 2013
a(n) = A078840(6,n).  R. J. Mathar, Jan 30 2019


MATHEMATICA

Select[Range[500], Plus @@ Last /@ FactorInteger[ # ] == 6 &] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2008 *)
Select[Range[1400], PrimeOmega[#]==6&] (* Harvey P. Dale, May 21 2012 *)


PROG

(PARI) is(n)=bigomega(n)==6 \\ Charles R Greathouse IV, Mar 21 2013


CROSSREFS

Cf. A046305, A120047 (number of 6almost primes <= 10^n).
Cf. 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), this sequence (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), 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: A046305 A114828 A036330 * A223086 A175163 A255990
Adjacent sequences: A046303 A046304 A046305 * A046307 A046308 A046309


KEYWORD

nonn


AUTHOR

Patrick De Geest, Jun 15 1998


STATUS

approved



