login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208060 a(n) = 1 + 2*n + 2^2*n*[n/2] + 2^3*n*[n/2]*[n/3] + 2^4*n*[n/2]*[n/3]*[n/4] + ... where [x]=floor(x). 3
1, 3, 13, 43, 233, 611, 4405, 10515, 64145, 218755, 1215821, 2689083, 28162105, 61179795, 307475813, 1236997051, 8042542625, 17101581699, 146671231501, 309740445795, 2415132010441, 8877053064643, 40919003272005, 85564885298027, 1068638260341937, 2783025471994851 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Compare the definition of a(n) to the exponential series:

exp(2*n) = 1 + 2*n + 2^2*n*(n/2) + 2^3*n*(n/2)*(n/3) + 2^4*n*(n/2)*(n/3)*(n/4) + ...

Conjecture: limit a(n)^(1/n) = 2*L where L = 2.200161058099... is the geometric mean of Luroth expansions, where log(L) = Sum_{n>=1} log(n)/(n*(n+1)) = 0.7885305659115... (cf. A085361).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = 1 + Sum_{m=1..n} Product_{k=1..m} 2^k*floor(n/k).

EXAMPLE

a(5) = 1 + 2*5+ 4*5[5/2] + 8*5[5/2][5/3] + 16*5[5/2][5/3][5/4] + 32*5[5/2][5/3][5/4][5/5] = 1 + 2*5 + 4*5*2 + 8*5*2*1 + 16*5*2*1*1 + 32*5*2*1*1*1 = 611.

PROG

(PARI) {a(n)=1+sum(m=1, n, prod(k=1, m, 2*floor(n/k)))}

(PARI) /* More efficient: variant of a program by Charles R Greathouse IV */

{a(n)=my(k=1); 1+sum(m=1, n, k*=2*(n\m))}

for(n=0, 60, print1(a(n), ", "))

CROSSREFS

Cf. A075885.

Sequence in context: A019008 A062609 A004660 * A284194 A209296 A193041

Adjacent sequences:  A208057 A208058 A208059 * A208061 A208062 A208063

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 23 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 29 14:50 EST 2021. Contains 349416 sequences. (Running on oeis4.)