A123322 Products of 8 distinct primes (squarefree 8-almost primes).

9699690, 11741730, 13123110, 14804790, 15825810, 16546530, 17160990, 17687670, 18888870, 20030010, 20281170, 20930910, 21111090, 21411390, 21637770, 21951930, 23130030, 23393370, 23993970, 24534510, 25555530, 25571910

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: A103936 A147713 A348072 * 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