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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.)