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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A014668 a(1) = 1, a(n) = Sum_{k=1..n-1} Sum_{d|k} a(d). 10
1, 1, 3, 7, 16, 33, 71, 143, 295, 594, 1206, 2413, 4871, 9743, 19559, 39138, 78428, 156857, 314047, 628095, 1256809, 2513693, 5028594, 10057189, 20116979, 40233975, 80472823, 160945945, 321901713, 643803427, 1287627061, 2575254123, 5150547536, 10301096282 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Equals eigensequence of triangle A010766 and starting (1, 3, 7, 16, 33,...) = row sums of triangle A163313. - Gary W. Adamson, Jul 30 2009. Gary Adamson's comment may be restated as "This sequence shifts left by one place under the floor transform." - N. J. A. Sloane, Feb 05 2016

The Gould & Quaintance reference, published in 2007, says incorrectly that this sequence is not in the OEIS. - Olivier Gérard, Oct 20 2011

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

H. W. Gould and J. Quaintance, Floor and Roof function analog of the Bell Numbers, INTEGERS, 7 (2007), #A58.

FORMULA

a(n) is asymptotic to c*2^n where c = 0.59960731361450033896934...

a(n+1) = Sum_{k=1..n} a(k)*floor(n/k). - Franklin T. Adams-Watters, Mar 21 2017

G.f. A(x) satisfies: A(x) = x * (1 + (1/(1 - x)) * Sum_{k>=1} A(x^k)). - Ilya Gutkovskiy, Feb 25 2020

MAPLE

with(numtheory):

a:= proc(n) option remember;

      `if`(n=1, 1, add(add(a(d), d=divisors(k)), k=1..n-1))

    end:

seq(a(n), n=1..40);  # Alois P. Heinz, Oct 28 2011

MATHEMATICA

a[1] = 1; a[n_] := a[n] = Sum[Sum[a[d], {d, Divisors[k]}], {k, 1, n-1}]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Apr 07 2015 *)

PROG

(PARI) // an=vector(100); a(n)=if(n<0, 0, an[n]); // an[1]=1; for(n=2, 100, an[n]=sum(k=1, n-1, sumdiv(k, d, a(d))))

CROSSREFS

Cf. A010766, A163313. - Gary W. Adamson, Jul 30 2009

Sequence in context: A277968 A217942 A002936 * A182615 A181893 A054455

Adjacent sequences:  A014665 A014666 A014667 * A014669 A014670 A014671

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jun 24 2003

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 30 12:04 EST 2020. Contains 338801 sequences. (Running on oeis4.)