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A046308 Numbers that are divisible by exactly 7 primes counting multiplicity. 53
128, 192, 288, 320, 432, 448, 480, 648, 672, 704, 720, 800, 832, 972, 1008, 1056, 1080, 1088, 1120, 1200, 1216, 1248, 1458, 1472, 1512, 1568, 1584, 1620, 1632, 1680, 1760, 1800, 1824, 1856, 1872, 1984, 2000, 2080, 2187, 2208, 2268, 2352, 2368, 2376 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Also called 7-almost primes. Products of exactly 7 primes (not necessarily distinct). - Jonathan Vos Post, Dec 11 2004
Also, positions of 7 in A001222. - Zak Seidov, Oct 14 2012
LINKS
Eric Weisstein's World of Mathematics, Reference
FORMULA
Product p_i^e_i with sum e_i = 7.
a(n) ~ 720n log n / (log log n)^6. - Charles R Greathouse IV, May 06 2013
a(n) = A078840(7,n). - R. J. Mathar, Jan 30 2019
MATHEMATICA
Select[Range[900], Plus @@ Last /@ FactorInteger[ # ] == 7 &] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2008 *)
PROG
(PARI) is(n)=bigomega(n)==7 \\ Charles R Greathouse IV, Mar 21 2013
CROSSREFS
Cf. A120048 (number of 7-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), A014613 (r = 4), A014614 (r = 5), A046306 (r = 6), this sequence (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: A114418 A046307 A036331 * A110290 A045028 A255997
KEYWORD
nonn
AUTHOR
Patrick De Geest, Jun 15 1998
STATUS
approved

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Last modified March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)