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 A132272 Product{k>0, 1+floor(n/10^k)}. 18
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 COMMENTS If n is written in base-10 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 (1+d(m)d(m-1)d(m-2)...d(2)d(1))*(1+d(m)d(m-1)d(m-2)...d(2))*...*(1+d(m)d(m-1)d(m-2))*(1+d(m)d(m-1))*(1+d(m)). a(n) = A179051(n) for n < 100. [From Reinhard Zumkeller, Jun 27 2010] LINKS FORMULA The following formulas are given for a general parameter p considering the product of terms 1+floor(n/p^k) for 0=1. a(p^m)=p^(m(m-1)/2)*product{0<=k=A067080(n)/((n+1)*product{00, 1+1/p^k}=2.2244691382741012... (for p=10 see constant A132325). a(n)>n^((1+log_p(n))/2)/(n+1)=p^A000217(log_p(n))/(n+1). lim sup n*a(n)/A067080(n)=2*product{k>0, 1+1/p^k}=2.2244691382741012..., for n-->oo (for p=10 see constant A132325). lim inf n*a(n)/A067080(n)=1/product{k>0, 1-1/p^k}=1/0.8900100999989990000001000..., for n-->oo (for p=10 s. constant A132038). lim inf a(n)/n^((1+log_p(n))/2)=1, for n-->oo. lim sup a(n)/n^((1+log_p(n))/2)=2*product{k>0, 1+1/p^k}=2.2244691382741012..., for n-->oo (for p=10 see constant A132325). lim inf a(n+1)/a(n)=2*product{k>0, 1+1/p^k}=2.2244691382741012... for n-->oo (for p=10 see constant A132325). EXAMPLE a(121)=(1+floor(121/10^1))*(1+floor(121/10^2))=13*2=26; a(132)=28 since 132=132(base-10) and so a(132)=(1+13)*(1+1)(base-10)=14*2=28. CROSSREFS Cf. A132038, A132270(p=2), A132271, A132325, A132328(p=3), A132271. For the product of terms floor(n/p^k) see A098844, A067080, A132027-A132033, A132263, A132264. Sequence in context: A226233 A329624 A059995 * A179051 A324160 A054899 Adjacent sequences:  A132269 A132270 A132271 * A132273 A132274 A132275 KEYWORD nonn,base AUTHOR Hieronymus Fischer, Aug 20 2007 STATUS approved

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Last modified April 5 11:49 EDT 2020. Contains 333241 sequences. (Running on oeis4.)