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A115343 Products of 9 distinct primes; also n has exactly 9 distinct prime factors and n is squarefree. 7
223092870, 281291010, 300690390, 340510170, 358888530, 363993630, 380570190, 397687290, 406816410, 417086670, 434444010, 455885430, 458948490, 481410930, 485555070, 497668710, 504894390, 512942430, 514083570, 531990690, 538047510, 547777230, 551861310 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi and Chai Wah Wu, Table of n, a(n) for n = 1..1045 (all terms with prime factors < 269 that are smaller than the first term with prime factor 269, first 1000 terms from Vincenzo Librandi)

EXAMPLE

514083570 is in the sequence as it is equal to 2*3*5*7*11*13*17*19*53.

MAPLE

N:= 10^9: # to get all terms < N

n0:= mul(ithprime(i), i=1..8):

Primes:= select(isprime, [$1..floor(N/n0)]):

nPrimes:= nops(Primes):

for i from 1 to 9 do

  for j from 1 to nPrimes do

    M[i, j]:= convert(Primes[1..min(j, i)], `*`);

od od:

A:= {}:

for i9 from 9 to nPrimes do

  m9:= Primes[i9];

for i8 in select(t -> M[7, t-1]*Primes[t]*m9 <= N, [$8..i9-1]) do

  m8:= m9*Primes[i8];

for i7 in select(t -> M[6, t-1]*Primes[t]*m8 <= N, [$7..i8-1]) do

  m7:= m8*Primes[i7];

for i6 in select(t -> M[5, t-1]*Primes[t]*m7 <= N, [$6..i7-1]) do

  m6:= m7*Primes[i6];

for i5 in select(t -> M[4, t-1]*Primes[t]*m6 <= N, [$5..i6-1]) do

  m5:= m6*Primes[i5];

for i4 in select(t -> M[3, t-1]*Primes[t]*m5 <= N, [$4..i5-1]) do

  m4:= m5*Primes[i4];

for i3 in select(t -> M[2, t-1]*Primes[t]*m4 <= N, [$3..i4-1]) do

  m3:= m4*Primes[i3];

for i2 in select(t -> M[1, t-1]*Primes[t]*m3 <= N, [$2..i3-1]) do

  m2:= m3*Primes[i2];

for i1 in select(t -> Primes[t]*m2 <= N, [$1..i2-1]) do

  A:= A union {m2*Primes[i1]};

od od od od od od od od od:

A; # Robert Israel, Sep 02 2014

MATHEMATICA

Module[{n=6*10^8, k}, k=PrimePi[n/Times@@Prime[Range[8]]]; Select[ Union[ Times@@@ Subsets[Prime[Range[k]], {9}]], #<=n&]](* Harvey P. Dale with suggestions from Jean-François Alcover, Sep 03 2014 *)

n = 10^9; n0 = Times @@ Prime[Range[8]]; primes = Select[Range[Floor[n/n0]], PrimeQ]; nPrimes = Length[primes]; Do[M[i, j] = Times @@ primes[[1 ;; Min[j, i]]], {i, 1, 9}, {j, 1, nPrimes}]; A = {};

Do[m9 = primes[[i9]];

Do[m8 = m9*primes[[i8]];

Do[m7 = m8*primes[[i7]];

Do[m6 = m7*primes[[i6]];

Do[m5 = m6*primes[[i5]];

Do[m4 = m5*primes[[i4]];

Do[m3 = m4*primes[[i3]];

Do[m2 = m3*primes[[i2]];

Do[A = A ~Union~ {m2*primes[[i1]]},

{i1, Select[Range[1, i2-1], primes[[#]]*m2 <= n &]}],

{i2, Select[Range[2, i3-1], M[1, #-1]*primes[[#]]*m3 <= n &]}],

{i3, Select[Range[3, i4-1], M[2, #-1]*primes[[#]]*m4 <= n &]}],

{i4, Select[Range[4, i5-1], M[3, #-1]*primes[[#]]*m5 <= n &]}],

{i5, Select[Range[5, i6-1], M[4, #-1]*primes[[#]]*m6 <= n &]}],

{i6, Select[Range[6, i7-1], M[5, #-1]*primes[[#]]*m7 <= n &]}],

{i7, Select[Range[7, i8-1], M[6, #-1]*primes[[#]]*m8 <= n &]}],

{i8, Select[Range[8, i9-1], M[7, #-1]*primes[[#]]*m9 <= n &]}],

{i9, 9, nPrimes}];

A (* Jean-François Alcover, Sep 03 2014, translated and adapted from Robert Israel's Maple program *)

PROG

(Python)

from operator import mul

from functools import reduce

from sympy import nextprime, sieve

from itertools import combinations

n = 190

m = 9699690*nextprime(n-1)

A115343 = []

for x in combinations(sieve.primerange(1, n), 9):

....y = reduce(mul, (d for d in x))

....if y < m:

........A115343.append(y)

A115343 = sorted(A115343) # Chai Wah Wu, Sep 02 2014

(PARI) is(n)=omega(n)==9 && bigomega(n)==9 \\ Hugo Pfoertner, Dec 18 2018

CROSSREFS

Sequence in context: A231093 A262559 A199498 * A258364 A046327 A206044

Adjacent sequences:  A115340 A115341 A115342 * A115344 A115345 A115346

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Mar 06 2006

EXTENSIONS

Corrected and extended by Don Reble, Mar 09 2006

More terms and corrected b-file from Chai Wah Wu, Sep 02 2014

STATUS

approved

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Last modified September 20 07:59 EDT 2019. Contains 327214 sequences. (Running on oeis4.)