

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
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OFFSET

1,1


COMMENTS

Also called 7almost 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

T. D. Noe, Table of n, a(n) for n = 1..10000
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 7almost primes <= 10^n).
Cf. A101605, A101606, A001222.
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), 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


KEYWORD

nonn


AUTHOR

Patrick De Geest, Jun 15 1998


STATUS

approved



