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 A122032 Product of the first n 3-almost primes, divided by product of the first n primes, rounded down. 3
 4, 16, 57, 164, 403, 870, 1535, 3393, 6492, 10075, 16250, 22837, 35092, 53862, 77929, 102925, 130837, 163010, 189773, 245903, 330117, 413691, 508391, 599788, 680172, 767719, 864615, 945420, 1075524, 1189739, 1217843, 1282919, 1376563, 1465693, 1505040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Note that this is nonmonotonic. What is the asymptotic value of the ratio A112141(n)/A002110(n)? Probably it can be easily proved that a(n) = 0 for n >= 116. - Giovanni Resta, Jun 13 2016 LINKS Giovanni Resta, Table of n, a(n) for n = 1..250 FORMULA a(n) = floor(A114425(n)/A002110(n)) = floor(Prod(i=1..n)3almostprime(i)/Prod(i=1..n)prime(i)) = floor(Prod(i=1..n)A014612(i)/Prod(i=1..n)A000040(i)) = floor(Prod(i=1..n)(A014612(i)/A000040(i))). EXAMPLE a(1) = floor(8/2) = floor(4) = 4. a(2) = floor(96/6) = floor(4) = 16. a(3) = floor(1728/30) = floor(57.6) = 57. a(4) = floor(34560/210) = floor(164.571429) = 164. a(5) = floor(933120/2310) = floor(403.948052) = 403. a(6) = floor(26127360/30030) = floor(870.041958) = 870. a(7) = floor(783820800/510510) = floor(1535.36816) = 1535. a(8) = floor(32920473600/9699690) = floor(3393.97172) = 3393. a(9) = floor(1448500838400/223092870) = floor(6492.81547) = 6492. a(10) = floor(65182537728000/6469693230) = floor(10075.058) = 10075. a(11) = floor(3259126886400000/200560490130) = floor(16250.0943) = 16250. a(12) = floor(169474598092800000/7420738134810) = floor(22837.9704) = 22837. MATHEMATICA tp = Select[Range[1000], PrimeOmega[#] == 3 &]; m = 1; Table[ Floor[m *= tp[[i]] / Prime[i]], {i, Length@ tp}] (* Giovanni Resta, Jun 13 2016 *) Floor[#[[1]]/#[[2]]]&/@Module[{nn=200, tap, len}, tap=FoldList[ Times, Select[ Range[ nn], PrimeOmega[#]==3&]]; len=Length[tap]; Thread[{tap, FoldList[Times, Prime[ Range[len]]]}]] (* Harvey P. Dale, Sep 08 2019 *) CROSSREFS Cf. A000040, A014612, A002110, A112141, A123389. Sequence in context: A197532 A220106 A281064 * A197674 A297220 A297375 Adjacent sequences: A122029 A122030 A122031 * A122033 A122034 A122035 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Oct 14 2006 EXTENSIONS a(10) corrected by and a(13)-a(35) from Giovanni Resta, Jun 13 2016 STATUS approved

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Last modified March 29 11:59 EDT 2023. Contains 361599 sequences. (Running on oeis4.)