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A123322 Products of 8 distinct primes (squarefree 8-almost primes). 3
9699690, 11741730, 13123110, 14804790, 15825810, 16546530, 17160990, 17687670, 18888870, 20030010, 20281170, 20930910, 21111090, 21411390, 21637770, 21951930, 23130030, 23393370, 23993970, 24534510, 25555530, 25571910 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection of A005117 and A046310.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..29422 (first 10000 terms from Rick Shepherd)

Index to sequences related to prime signature

EXAMPLE

a(1) = 9699690 = 2*3*5*7*11*13*17*19 = A002110(8).

MAPLE

N:= 3*10^7: # to get all terms  <= N

pmax:= floor(N/mul(ithprime(i), i=1..7)):

Primes:= select(isprime, [2, seq(i, i=3..pmax, 2)]):

sort(select(`<`, map(convert, combinat:-choose(Primes, 8), `*`), N)); # Robert Israel, Dec 18 2018

MATHEMATICA

f8Q[n_]:=Last/@FactorInteger[n]=={1, 1, 1, 1, 1, 1, 1, 1}; lst={}; Do[If[f8Q[n], AppendTo[lst, n]], {n, 10!, 11!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 26 2008 *)

Take[ Sort[ Times @@@ Subsets[ Prime@ Range@ 15, {8}]], 22] (* Robert G. Wilson v, Dec 18 2018 *)

PROG

(PARI) is(n)=issquarefree(n)&&omega(n)==8 \\ Charles R Greathouse IV, Feb 01 2017, corrected (following an observation from Zak Seidov) by M. F. Hasler, Dec 19 2018

(PARI) is(n) = my(f = factor(n)); omega(f) == 8 && bigomega(f) == 8 \\ David A. Corneth, Dec 18 2018

CROSSREFS

Cf. A001221, A001222, A005117, A046310, A048692, Squarefree k-almost primes: A000040 (k=1), A006881 (k=2), A007304 (k=3), A046386 (k=4), A046387 (k=5), A067885 (k=6), A123321 (k=7), A115343 (k=9).

Sequence in context: A251504 A103936 A147713 * A258363 A147575 A046326

Adjacent sequences:  A123319 A123320 A123321 * A123323 A123324 A123325

KEYWORD

nonn

AUTHOR

Rick L. Shepherd, Sep 25 2006

EXTENSIONS

Edited by Robert Israel, Dec 18 2018

STATUS

approved

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Last modified August 15 00:52 EDT 2020. Contains 336484 sequences. (Running on oeis4.)