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A014613 Numbers that are products of 4 primes. 143
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
J. H. Conway, Heiko Dietrich and E. A. O'Brien, Counting groups: gnus, moas and other exotica, Math. Intell., Vol. 30, No. 2, Spring 2008.
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
a(n) = A078840(4,n). - R. J. Mathar, Jan 30 2019
MATHEMATICA
Select[Range[200], Plus @@ Last /@ FactorInteger[ # ] == 4 &] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2008 *)
Select[Range[400], PrimeOmega[#] == 4&] (* Jean-François Alcover, Jan 17 2014 *)
PROG
(PARI) isA014613(n) = bigomega(n)==4 \\ Michael B. Porter, Dec 13 2009
(Python)
from sympy import factorint
def ok(n): return sum(factorint(n).values()) == 4
print([k for k in range(377) if ok(k)]) # Michael S. Branicky, Nov 19 2021
CROSSREFS
Cf. A033987, A114106 (number of 4-almost primes <= 10^n).
Sequences listing r-almost 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 * A323350 A307341 A046370
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Patrick De Geest, Jun 15 1998
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)