

A014613


Numbers that are products of 4 primes (these numbers are sometimes called "4almost primes", a generalization of semiprimes).


127



16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, 104, 126, 132, 135, 136, 140, 150, 152, 156, 184, 189, 196, 198, 204, 210, 220, 225, 228, 232, 234, 248, 250, 260, 276, 294, 296, 297, 306, 308, 315, 328, 330, 340, 342, 344, 348, 350, 351, 364, 372, 375, 376
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OFFSET

1,1


COMMENTS

Also called "quadruprimes". Divisible by exactly 4 prime powers (not including 1).


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 = 4.
a(n) ~ 6n log n / (log log n)^3.  Charles R Greathouse IV, May 04 2013


MATHEMATICA

Select[Range[200], Plus @@ Last /@ FactorInteger[ # ] == 4 &] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2008 *)
Select[Range[400], PrimeOmega[#] == 4&] (* JeanFrançois Alcover, Jan 17 2014 *)


PROG

(PARI) isA014613(n) = bigomega(n)==4 \\ Michael B. Porter, Dec 13 2009


CROSSREFS

Cf. A033987, A114106 (number of 4almost primes <= 10^n).
Sequences listing ralmost primes, that is, the n such that A001222(n) = r: A000040 (r = 1), A001358 (r = 2), A014612 (r = 3), this sequence (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), 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: A036328 A067028 A110893 * A046370 A103248 A286195
Adjacent sequences: A014610 A014611 A014612 * A014614 A014615 A014616


KEYWORD

nonn


AUTHOR

Eric W. Weisstein


EXTENSIONS

More terms from Patrick De Geest, Jun 15 1998


STATUS

approved



