login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A046314 Numbers that are divisible by exactly 10 primes with multiplicity. 46
1024, 1536, 2304, 2560, 3456, 3584, 3840, 5184, 5376, 5632, 5760, 6400, 6656, 7776, 8064, 8448, 8640, 8704, 8960, 9600, 9728, 9984, 11664, 11776, 12096, 12544, 12672, 12960, 13056, 13440, 14080, 14400, 14592, 14848, 14976, 15872, 16000, 16640 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Also called 10-almost primes. Products of exactly 10 primes (not necessarily distinct). Any 10-almost prime can be represented in several ways as a product of two 5-almost primes A014614 and in several ways as a product of five semiprimes A001358. - Jonathan Vos Post, Dec 11 2004
LINKS
Eric Weisstein's World of Mathematics, Reference
FORMULA
Product p_i^e_i with Sum e_i = 10.
a(n) ~ 362880n log n / (log log n)^9. - Charles R Greathouse IV, May 06 2013
MATHEMATICA
Select[Range[5000], Plus @@ Last /@ FactorInteger[ # ] == 10 &] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2008 *)
Select[Range[17000], PrimeOmega[#]==10&] (* Harvey P. Dale, Jun 23 2018 *)
PROG
(PARI) is(n)=bigomega(n)==10 \\ Charles R Greathouse IV, Mar 21 2013
CROSSREFS
Cf. A046313, A120051 (number of 10-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), A046308 (r = 7), A046310 (r = 8), A046312 (r = 9), this sequence (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: A074211 A057443 A046313 * A221260 A223065 A298607
KEYWORD
nonn
AUTHOR
Patrick De Geest, Jun 15 1998
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 07:25 EDT 2024. Contains 370955 sequences. (Running on oeis4.)