A115343 Products of 9 distinct primes.

223092870, 281291010, 300690390, 340510170, 358888530, 363993630, 380570190, 397687290, 406816410, 417086670, 434444010, 455885430, 458948490, 481410930, 485555070, 497668710, 504894390, 512942430, 514083570, 531990690, 538047510, 547777230, 551861310

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1045 terms from Vincenzo Librandi and Chai Wah Wu)

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

Cf. A000040, A006881, A007304, A046386, A046387, A067885, A123321, A123322, A115343, A281222.

Sequence in context: A262559 A199498 A348073 * A258364 A046327 A206044

Adjacent sequences: A115340 A115341 A115342 * A115344 A115345 A115346

Keyword

nonn,easy

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