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 A132032 Product{0<=k<=floor(log_8(n)), floor(n/8^k)}, n>=1. 4
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 32, 34, 36, 38, 40, 42, 44, 46, 72, 75, 78, 81, 84, 87, 90, 93, 128, 132, 136, 140, 144, 148, 152, 156, 200, 205, 210, 215, 220, 225, 230, 235, 288, 294, 300, 306, 312, 318, 324, 330, 392, 399, 406, 413, 420, 427, 434 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If n is written in base-8 as n=d(m)d(m-1)d(m-2)...d(2)d(1)d(0) (where d(k) is the digit at position k) then a(n) is also the product d(m)d(m-1)d(m-2)...d(2)d(1)d(0)*d(m)d(m-1)d(m-2)...d(2)d(1)*d(m)d(m-1)d(m-2)...d(2)*...*d(m)d(m-1)d(m-2)*d(m)d(m-1)*d(m). LINKS FORMULA Recurrence: a(n)=n*a(floor(n/8)); a(n*8^m)=n^m*8^(m(m+1)/2)*a(n). a(k*8^m)=k^(m+1)*8^(m(m+1)/2), for 0=0. b(n) can also be written n^(1+floor(log_8(n)))/8^A000217(floor(log_8(n))). Also: a(n)<=3^((1-log_8(3))/2)*n^((1+log_8(n))/2) = 1.295758534...*8^A000217(log_8(n)), equality holds for n=3*8^m, m>=0. a(n)>c*b(n), where c = 0.46456888368647639098... (see constant A132024). Also: a(n)>c*2^(1/3)*n^((1+log_8(n))/2)=0.4645688836...*1.25992105...*8^A000217(log_8(n)). lim inf a(n)/b(n)=0.46456888368647639098..., for n-->oo. lim sup a(n)/b(n)=1, for n-->oo. lim inf a(n)/n^((1+log_8(n))/2)=0.46456888368647639098...*2^(1/3), for n-->oo. lim sup a(n)/n^((1+log_8(n))/2)=sqrt(3)/3^log_8(sqrt(3))=1.295758534..., for n-->oo. lim inf a(n)/a(n+1)=0.46456888368647639098... for n-->oo (see constant A132024). EXAMPLE a(70)=floor(70/8^0)*floor(70/8^1)*floor(70/8^2)=70*8*1=560; For n=75, 75=113(base-8) and so a(75)=113*11*1(base-8)=75*9*1=675. CROSSREFS Cf. A048651, A132024, A132036, A000217. For formulas regarding a general parameter p (i.e. terms floor(n/p^k)) see A132264. For the product of terms floor(n/p^k) for p=2 to p=12 see A098844(p=2), A132027(p=3)-A132033(p=9), A067080(p=10), A132263(p=11), A132264(p=12). For the products of terms 1+floor(n/p^k) see A132269-A132272, A132327, A132328. Sequence in context: A032950 A248502 A250039 * A055645 A262545 A043320 Adjacent sequences:  A132029 A132030 A132031 * A132033 A132034 A132035 KEYWORD nonn AUTHOR Hieronymus Fischer, Aug 20 2007 STATUS approved

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Last modified May 26 19:44 EDT 2019. Contains 323597 sequences. (Running on oeis4.)