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A046308
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Numbers that are divisible by exactly 7 primes counting multiplicity.
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53
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Reference
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FORMULA
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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
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MATHEMATICA
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Select[Range[900], Plus @@ Last /@ FactorInteger[ # ] == 7 &] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2008 *)
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PROG
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(PARI) is(n)=bigomega(n)==7 \\ Charles R Greathouse IV, Mar 21 2013
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CROSSREFS
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Cf. A120048 (number of 7-almost primes <= 10^n).
Cf. A101605, A101606, A001222.
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
Adjacent sequences: A046305 A046306 A046307 * A046309 A046310 A046311
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KEYWORD
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nonn
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AUTHOR
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Patrick De Geest, Jun 15 1998
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STATUS
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approved
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